129:@0.918240:0.967835:0.943652:0.967835:0.943652:0.951847:0.918240:0.951847:0.000000:0.000000:0.000000 Ecuación de la forma :@0.108231:0.100565:0.279785:0.100565:0.279785:0.082883:0.108231:0.082883:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ax bcxd:@0.296815:0.101343:0.397173:0.101343:0.397173:0.084874:0.296815:0.084874:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 =:@0.343145:0.101227:0.353953:0.101227:0.353953:0.084730:0.343145:0.084730:0.000000 +:@0.316289:0.101863:0.268646:0.101863:0.268646:0.085583:0.316289:0.085583:0.000000 +:@0.374509:0.101863:0.326866:0.101863:0.326866:0.085583:0.374509:0.085583:0.000000 Ejercicios resueltos:@0.108231:0.124778:0.238886:0.124778:0.238886:0.107991:0.108231:0.107991:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1.:@0.108231:0.146365:0.120503:0.146365:0.120503:0.129650:0.108231:0.129650:0.000000:0.000000 Hallar , si existe solución de la ecuación 2:@0.120503:0.146148:0.494219:0.144896:0.494219:0.128398:0.120503:0.129650:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.178260:0.146264:0.185735:0.146264:0.185735:0.129795:0.178260:0.129795:0.000000 :@0.191013:0.145931:0.207061:0.145931:0.207061:0.131284:0.191013:0.131284:0.000000 R:@0.212341:0.145179:0.226250:0.145179:0.226250:0.131732:0.212341:0.131732:0.000000 x:@0.495617:0.145011:0.503092:0.145011:0.503092:0.128543:0.495617:0.128543:0.000000 x:@0.558499:0.145011:0.565974:0.145011:0.565974:0.128543:0.558499:0.128543:0.000000 −:@0.506502:0.145532:0.517079:0.145532:0.517079:0.129251:0.506502:0.129251:0.000000 − +:@0.546188:0.145532:0.579960:0.145532:0.579960:0.129251:0.546188:0.129251:0.000000:0.000000:0.000000 3 =:@0.519803:0.144896:0.543332:0.144896:0.543332:0.128398:0.519803:0.128398:0.000000:0.000000:0.000000 1. :@0.581901:0.144896:0.599914:0.146154:0.599914:0.129656:0.581901:0.128398:0.000000:0.000000:0.000000:0.000000:0.000000 En primer lugar, la raíz cuadrada de números reales está bien :@0.131691:0.163504:0.599818:0.163504:0.599818:0.147006:0.131691:0.147007:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 definida para números reales no negativos. En consecuencia, :@0.131684:0.180855:0.599918:0.180855:0.599918:0.164357:0.131684:0.164357:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 – 3 ≥ 0, de donde :@0.131684:0.208891:0.299675:0.208891:0.299675:0.192393:0.131684:0.192393:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.140180:0.209006:0.147655:0.209006:0.147655:0.192537:0.140180:0.192537:0.000000 x:@0.305310:0.207751:0.312785:0.207751:0.312785:0.191282:0.305310:0.191282:0.000000 ≥:@0.316927:0.208271:0.327503:0.208271:0.327503:0.191990:0.316927:0.191990:0.000000 3:@0.332262:0.198324:0.340758:0.198324:0.340758:0.181826:0.332262:0.181826:0.000000 2:@0.332062:0.218636:0.340558:0.218636:0.340558:0.202139:0.332062:0.202139:0.000000 , o bien :@0.344469:0.208892:0.439466:0.208892:0.439466:0.192395:0.344469:0.192395:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 xx:@0.405771:0.209008:0.421563:0.208780:0.421563:0.192312:0.405771:0.192539:0.000000:0.000000 :@0.419276:0.208676:0.435324:0.208676:0.435324:0.194029:0.419276:0.194029:0.000000 ∈:@0.425301:0.209301:0.439037:0.209301:0.439037:0.193020:0.425301:0.193020:0.000000 ∞:@0.467241:0.209301:0.480977:0.209301:0.480977:0.193020:0.467241:0.193020:0.000000 3:@0.448958:0.199353:0.457454:0.199353:0.457454:0.182856:0.448958:0.182856:0.000000 2:@0.448746:0.219668:0.457242:0.219668:0.457242:0.203170:0.448746:0.203170:0.000000 ,:@0.461211:0.208665:0.463966:0.208665:0.463966:0.192167:0.461211:0.192167:0.000000 . . Además, para :@0.491361:0.208665:0.599897:0.208892:0.599897:0.192395:0.491361:0.192167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ≥:@0.146656:0.240960:0.157233:0.240960:0.157233:0.224679:0.146656:0.224679:0.000000 − ≥:@0.216435:0.240960:0.252303:0.240960:0.252303:0.224679:0.216435:0.224679:0.000000:0.000000:0.000000 x:@0.135402:0.240439:0.142877:0.240439:0.142877:0.223971:0.135402:0.223971:0.000000 x:@0.205971:0.240439:0.213446:0.240439:0.213446:0.223971:0.205971:0.223971:0.000000 3:@0.162467:0.231445:0.170963:0.231445:0.170963:0.214947:0.162467:0.214947:0.000000 2:@0.162258:0.251719:0.170754:0.251719:0.170754:0.235221:0.162258:0.235221:0.000000 ,2:@0.174770:0.240324:0.204574:0.240324:0.204574:0.223826:0.174770:0.223826:0.000000:0.000000 30, con lo que la igualdad 2:@0.228952:0.240324:0.458572:0.241582:0.458572:0.225085:0.228952:0.223826:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.459955:0.241698:0.467430:0.241698:0.467430:0.225229:0.459955:0.225229:0.000000 x:@0.522836:0.241698:0.530311:0.241698:0.530311:0.225229:0.522836:0.225229:0.000000 −:@0.470844:0.242218:0.481420:0.242218:0.481420:0.225938:0.470844:0.225938:0.000000 − +:@0.510530:0.242218:0.544302:0.242218:0.544302:0.225938:0.510530:0.225938:0.000000:0.000000:0.000000 3 =:@0.484156:0.241582:0.507670:0.241582:0.507670:0.225085:0.484156:0.225085:0.000000:0.000000:0.000000 1 tiene :@0.546239:0.241582:0.599906:0.241582:0.599906:0.225085:0.546239:0.225085:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 sentido si y solo si :@0.131683:0.269618:0.267116:0.269618:0.267116:0.253120:0.131683:0.253120:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 10, :@0.302558:0.268363:0.379859:0.269620:0.379859:0.253122:0.302558:0.251865:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3 3:@0.393910:0.259443:0.395968:0.260080:0.395968:0.243582:0.393910:0.242946:0.000000:0.000000:0.000000 2 2:@0.393698:0.279802:0.395756:0.280394:0.395756:0.263897:0.393698:0.263304:0.000000:0.000000:0.000000 , ,:@0.406471:0.268365:0.402480:0.269391:0.402480:0.252894:0.406471:0.251867:0.000000:0.000000:0.000000 . . .:@0.433539:0.268365:0.429428:0.269620:0.429428:0.253122:0.433539:0.251867:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.281189:0.268480:0.288664:0.268480:0.288664:0.252012:0.281189:0.252012:0.000000 x x x:@0.356940:0.268480:0.360077:0.269507:0.360077:0.253038:0.356940:0.252012:0.000000:0.000000:0.000000:0.000000:0.000000 −+≥:@0.269681:0.268999:0.322988:0.268999:0.322988:0.252718:0.269681:0.252718:0.000000:0.000000:0.000000 ∈ ∈:@0.368781:0.268999:0.377550:0.270027:0.377550:0.253747:0.368781:0.252718:0.000000:0.000000:0.000000 ∞:@0.411859:0.268999:0.425595:0.268999:0.425595:0.252718:0.411859:0.252718:0.000000 :@0.359669:0.269403:0.375717:0.269403:0.375717:0.254756:0.359669:0.254756:0.000000 ∞:@0.405755:0.270027:0.419491:0.270027:0.419491:0.253747:0.405755:0.253747:0.000000 :@0.108237:0.304784:0.112379:0.304784:0.112379:0.288287:0.108237:0.288287:0.000000 Sea :@0.131683:0.304784:0.197801:0.304784:0.197801:0.288287:0.131683:0.288287:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x x:@0.162970:0.304900:0.181032:0.304674:0.181032:0.288205:0.162970:0.288431:0.000000:0.000000:0.000000 :@0.177611:0.304567:0.193659:0.304567:0.193659:0.289920:0.177611:0.289920:0.000000 ∈:@0.184770:0.305194:0.198506:0.305194:0.198506:0.288913:0.184770:0.288913:0.000000 ∞:@0.226710:0.305194:0.240446:0.305194:0.240446:0.288913:0.226710:0.288913:0.000000 3:@0.208427:0.295246:0.216923:0.295246:0.216923:0.278749:0.208427:0.278749:0.000000 2:@0.208216:0.315561:0.216712:0.315561:0.216712:0.299063:0.208216:0.299063:0.000000 ,:@0.220680:0.304558:0.223435:0.304558:0.223435:0.288060:0.220680:0.288060:0.000000 . , entonces :@0.250830:0.304558:0.326400:0.304785:0.326400:0.288288:0.250830:0.288060:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.333134:0.303644:0.340609:0.303644:0.340609:0.287175:0.333134:0.287175:0.000000 ≥:@0.344751:0.304164:0.355328:0.304164:0.355328:0.287884:0.344751:0.287884:0.000000 3:@0.360086:0.294217:0.368582:0.294217:0.368582:0.277719:0.360086:0.277719:0.000000 2:@0.359884:0.314530:0.368380:0.314530:0.368380:0.298032:0.359884:0.298032:0.000000 . Multiplicando por –1 a esta :@0.371611:0.303528:0.599923:0.304786:0.599923:0.288288:0.371611:0.287031:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 última desigualdad, se obtiene :@0.131701:0.332822:0.352254:0.332821:0.352254:0.316324:0.131701:0.316324:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.368063:0.331682:0.375538:0.331682:0.375538:0.315213:0.368063:0.315213:0.000000 −≤ −:@0.355752:0.332202:0.404281:0.332202:0.404281:0.315921:0.355752:0.315921:0.000000:0.000000:0.000000:0.000000 3:@0.407634:0.322254:0.416130:0.322254:0.416130:0.305757:0.407634:0.305757:0.000000 2:@0.407431:0.342567:0.415927:0.342567:0.415927:0.326070:0.407431:0.326070:0.000000 , y sumando 1 en ambos :@0.420315:0.332823:0.599925:0.332823:0.599925:0.316326:0.420315:0.316326:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 miembros, se tiene :@0.131683:0.360859:0.271333:0.360859:0.271333:0.344362:0.131683:0.344362:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.287531:0.359719:0.295006:0.359719:0.295006:0.343251:0.287531:0.343251:0.000000 −+ ≤−:@0.275220:0.360240:0.345577:0.360240:0.345577:0.343959:0.275220:0.343959:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.310919:0.359604:0.319415:0.359604:0.319415:0.343106:0.310919:0.343106:0.000000 1:@0.349353:0.350292:0.357849:0.350292:0.357849:0.333795:0.349353:0.333795:0.000000 2:@0.348729:0.370605:0.357225:0.370605:0.357225:0.354108:0.348729:0.354108:0.000000 . Así, :@0.360455:0.359604:0.400219:0.360862:0.400219:0.344364:0.360455:0.343106:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.416407:0.360977:0.423882:0.360977:0.423882:0.344508:0.416407:0.344508:0.000000 x xx:@0.500692:0.360977:0.526416:0.360749:0.526416:0.344280:0.500692:0.344508:0.000000:0.000000:0.000000:0.000000 −+ ≤−:@0.404106:0.361497:0.474462:0.361497:0.474462:0.345217:0.404106:0.345217:0.000000:0.000000:0.000000:0.000000:0.000000 ∈ ∈:@0.511895:0.361497:0.543890:0.361270:0.543890:0.344989:0.511895:0.345217:0.000000:0.000000:0.000000 ∞ ∞:@0.553836:0.361497:0.585830:0.361270:0.585830:0.344989:0.553836:0.345217:0.000000:0.000000:0.000000 1:@0.439808:0.360861:0.448304:0.360861:0.448304:0.344363:0.439808:0.344363:0.000000 1:@0.478242:0.351550:0.486738:0.351550:0.486738:0.335052:0.478242:0.335052:0.000000 2:@0.477607:0.371864:0.486103:0.371864:0.486103:0.355367:0.477607:0.355367:0.000000 3 3:@0.535558:0.351550:0.562308:0.351322:0.562308:0.334824:0.535558:0.335052:0.000000:0.000000:0.000000 2 2:@0.535346:0.371864:0.562096:0.371637:0.562096:0.355139:0.535346:0.355367:0.000000:0.000000:0.000000 , :@0.547811:0.360861:0.545287:0.360861:0.545287:0.344363:0.547811:0.344363:0.000000:0.000000:0.000000 , ,:@0.578693:0.360861:0.568819:0.360634:0.568819:0.344136:0.578693:0.344363:0.000000:0.000000:0.000000 , :@0.489630:0.360861:0.524192:0.360861:0.524192:0.344363:0.489630:0.344363:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.525097:0.360644:0.541145:0.360644:0.541145:0.345997:0.525097:0.345997:0.000000 . , :@0.596214:0.360634:0.599908:0.360861:0.599908:0.344363:0.596214:0.344136:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 es decir que – + 1 es negativo para :@0.131685:0.393553:0.432377:0.393553:0.432377:0.377055:0.131685:0.377055:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.234600:0.393668:0.242075:0.393668:0.242075:0.377200:0.234600:0.377200:0.000000 xx:@0.399510:0.393668:0.413683:0.393439:0.413683:0.376970:0.399510:0.377200:0.000000:0.000000 :@0.412187:0.393336:0.428235:0.393336:0.428235:0.378689:0.412187:0.378689:0.000000 ∈:@0.417420:0.393960:0.431156:0.393960:0.431156:0.377679:0.417420:0.377679:0.000000 ∞:@0.459361:0.393960:0.473097:0.393960:0.473097:0.377679:0.459361:0.377679:0.000000 3:@0.441078:0.384012:0.449574:0.384012:0.449574:0.367514:0.441078:0.367514:0.000000 2:@0.440866:0.404327:0.449362:0.404327:0.449362:0.387829:0.440866:0.387829:0.000000 ,:@0.453331:0.393323:0.456086:0.393323:0.456086:0.376826:0.453331:0.376826:0.000000 . , lo que significa :@0.483481:0.393323:0.599895:0.393551:0.599895:0.377053:0.483481:0.376826:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 que la igualdad 2:@0.131672:0.426243:0.271917:0.426241:0.271917:0.409743:0.131672:0.409745:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.273299:0.426356:0.280774:0.426356:0.280774:0.409888:0.273299:0.409888:0.000000 x:@0.336181:0.426356:0.343656:0.426356:0.343656:0.409888:0.336181:0.409888:0.000000 −:@0.284189:0.426877:0.294765:0.426877:0.294765:0.410596:0.284189:0.410596:0.000000 − +:@0.323875:0.426877:0.357647:0.426877:0.357647:0.410596:0.323875:0.410596:0.000000:0.000000:0.000000 3 =:@0.297501:0.426241:0.321016:0.426241:0.321016:0.409743:0.297501:0.409743:0.000000:0.000000:0.000000 1 es contradictoria. Por lo tanto, :@0.359585:0.426241:0.599890:0.426241:0.599890:0.409743:0.359585:0.409743:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la ecuación propuesta 2:@0.131691:0.446353:0.316679:0.447615:0.316679:0.431117:0.131691:0.429855:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.318062:0.447731:0.325537:0.447731:0.325537:0.431262:0.318062:0.431262:0.000000 x:@0.380944:0.447731:0.388419:0.447731:0.388419:0.431262:0.380944:0.431262:0.000000 −:@0.328951:0.448251:0.339528:0.448251:0.339528:0.431970:0.328951:0.431970:0.000000 − +:@0.368637:0.448251:0.402409:0.448251:0.402409:0.431970:0.368637:0.431970:0.000000:0.000000:0.000000 3 =:@0.342263:0.447615:0.365777:0.447615:0.365777:0.431117:0.342263:0.431117:0.000000:0.000000:0.000000 1 no tiene solución en .:@0.404346:0.447615:0.585007:0.446358:0.585007:0.429860:0.404346:0.431117:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.568343:0.445389:0.582252:0.445389:0.582252:0.431942:0.568343:0.431942:0.000000 :@0.108233:0.473974:0.112375:0.473974:0.112375:0.457477:0.108233:0.457477:0.000000 Sean , las funciones definidas por ()=2:@0.131679:0.473974:0.457530:0.473979:0.457530:0.457482:0.131679:0.457477:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u v:@0.169033:0.474090:0.192460:0.474090:0.192460:0.457621:0.169033:0.457621:0.000000:0.000000:0.000000 ux:@0.390183:0.474095:0.413513:0.474095:0.413513:0.457626:0.390183:0.457626:0.000000:0.000000 x:@0.458921:0.474095:0.466396:0.474095:0.466396:0.457626:0.458921:0.457626:0.000000 v x:@0.499282:0.474095:0.521781:0.474095:0.521781:0.457626:0.499282:0.457626:0.000000:0.000000:0.000000 x:@0.556979:0.474095:0.564454:0.474095:0.564454:0.457626:0.556979:0.457626:0.000000 −:@0.469803:0.474615:0.480380:0.474615:0.480380:0.458335:0.469803:0.458335:0.000000 − +:@0.544668:0.474615:0.578438:0.474615:0.578438:0.458335:0.544668:0.458335:0.000000:0.000000:0.000000 3, ()=:@0.483114:0.473979:0.541814:0.473979:0.541814:0.457482:0.483114:0.457482:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1. :@0.580383:0.473979:0.599899:0.473979:0.599899:0.457482:0.580383:0.457482:0.000000:0.000000:0.000000:0.000000:0.000000 Se tiene :@0.131676:0.502897:0.192485:0.502897:0.192485:0.486399:0.131676:0.486399:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Domu x:@0.195650:0.503013:0.248425:0.502785:0.248425:0.486316:0.195650:0.486544:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 °:@0.294228:0.503533:0.301934:0.503533:0.301934:0.487253:0.294228:0.487253:0.000000 ()= :@0.229628:0.502897:0.267596:0.502897:0.267596:0.486399:0.229628:0.486399:0.000000:0.000000:0.000000:0.000000 3 3:@0.275953:0.493586:0.284317:0.493358:0.284317:0.476860:0.275953:0.477088:0.000000:0.000000:0.000000 2 2:@0.275741:0.513900:0.284105:0.513673:0.284105:0.497175:0.275741:0.497403:0.000000:0.000000:0.000000 , ,:@0.288206:0.502897:0.290828:0.502670:0.290828:0.486172:0.288206:0.486399:0.000000:0.000000:0.000000 , . , :@0.319088:0.502897:0.321917:0.502897:0.321917:0.486399:0.319088:0.486399:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ∈:@0.252163:0.503306:0.265899:0.503306:0.265899:0.487025:0.252163:0.487025:0.000000 ∞:@0.294103:0.503306:0.307840:0.503306:0.307840:0.487025:0.294103:0.487025:0.000000 Domv:@0.325089:0.503013:0.371981:0.503013:0.371981:0.486544:0.325089:0.486544:0.000000:0.000000:0.000000:0.000000 ()=:@0.359073:0.502897:0.391709:0.502897:0.391709:0.486399:0.359073:0.486399:0.000000:0.000000:0.000000 . En la figura 3.9. se mues-:@0.412978:0.502897:0.595747:0.502897:0.595747:0.486399:0.412978:0.486399:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tran las gráficas de las funciones y , se ve que no se cortan.:@0.131666:0.531815:0.564104:0.531815:0.564104:0.515317:0.131666:0.515317:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u v:@0.362316:0.531931:0.395414:0.531931:0.395414:0.515462:0.362316:0.515462:0.000000:0.000000:0.000000 2.:@0.108230:0.559649:0.120502:0.559649:0.120502:0.542934:0.108230:0.542934:0.000000:0.000000 Considérese la ecuación y 2:@0.120503:0.559432:0.400176:0.559437:0.400176:0.542939:0.120503:0.542934:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.305967:0.559547:0.313442:0.559547:0.313442:0.543079:0.305967:0.543079:0.000000 :@0.317584:0.559215:0.333632:0.559215:0.333632:0.544568:0.317584:0.544568:0.000000 R:@0.337776:0.558463:0.351686:0.558463:0.351686:0.545016:0.337776:0.545016:0.000000 x:@0.401574:0.559552:0.409049:0.559552:0.409049:0.543084:0.401574:0.543084:0.000000 x:@0.452878:0.559552:0.460353:0.559552:0.460353:0.543084:0.452878:0.543084:0.000000 −:@0.412459:0.560073:0.371732:0.560073:0.371732:0.543792:0.412459:0.543792:0.000000 −:@0.463762:0.560073:0.423036:0.560073:0.423036:0.543792:0.463762:0.543792:0.000000 3 =:@0.425760:0.559437:0.449289:0.559437:0.449289:0.542939:0.425760:0.542939:0.000000:0.000000:0.000000 1.:@0.476280:0.559437:0.487463:0.559437:0.487463:0.542939:0.476280:0.542939:0.000000:0.000000 :@0.108231:0.586584:0.112373:0.586584:0.112373:0.570087:0.108231:0.570087:0.000000 Sean , las funciones reales definidas por :@0.131685:0.586584:0.417779:0.586584:0.417779:0.570087:0.131685:0.570087:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u v:@0.167499:0.586700:0.190155:0.586700:0.190155:0.570231:0.167499:0.570231:0.000000:0.000000:0.000000 ux:@0.418895:0.586749:0.440610:0.586749:0.440610:0.570608:0.418895:0.570608:0.000000:0.000000 x:@0.482876:0.586749:0.489833:0.586749:0.489833:0.570608:0.482876:0.570608:0.000000 v x:@0.520443:0.586749:0.541388:0.586749:0.541388:0.570608:0.520443:0.570608:0.000000:0.000000:0.000000 x:@0.563372:0.586749:0.570330:0.586749:0.570330:0.570608:0.563372:0.570608:0.000000 −:@0.493007:0.587259:0.422355:0.587259:0.422355:0.571302:0.493007:0.571302:0.000000 −:@0.573504:0.587259:0.502852:0.587259:0.502852:0.571302:0.573504:0.571302:0.000000 ()=2:@0.427412:0.586635:0.481567:0.586635:0.481567:0.570466:0.427412:0.570466:0.000000:0.000000:0.000000:0.000000 3, ()=:@0.505380:0.586635:0.560037:0.586635:0.560037:0.570466:0.505380:0.570466:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1.:@0.585159:0.586635:0.595560:0.586635:0.595560:0.570466:0.585159:0.570466:0.000000:0.000000 :@0.595765:0.586584:0.599907:0.586584:0.599907:0.570087:0.595765:0.570087:0.000000 :@0.108239:0.614620:0.112381:0.614620:0.112381:0.598122:0.108239:0.598122:0.000000 Entonces :@0.131692:0.614620:0.200828:0.614620:0.200828:0.598122:0.131692:0.598122:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Domu x:@0.202591:0.614738:0.253955:0.614510:0.253955:0.598042:0.202591:0.598269:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 °:@0.301169:0.615258:0.308875:0.615258:0.308875:0.598978:0.301169:0.598978:0.000000 ()= ,:@0.236566:0.614622:0.296358:0.614395:0.296358:0.597897:0.236566:0.598124:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3 3:@0.282894:0.605311:0.289847:0.605083:0.289847:0.588585:0.282894:0.588813:0.000000:0.000000:0.000000 2 2:@0.282682:0.625625:0.289635:0.625398:0.289635:0.608900:0.282682:0.609128:0.000000:0.000000:0.000000 ,:@0.295146:0.614622:0.297901:0.614622:0.297901:0.598124:0.295146:0.598124:0.000000 , . , :@0.326028:0.614622:0.327447:0.614622:0.327447:0.598124:0.326028:0.598124:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ∈:@0.257693:0.615031:0.271429:0.615031:0.271429:0.598750:0.257693:0.598750:0.000000 ∞:@0.299633:0.615031:0.313370:0.615031:0.313370:0.598750:0.299633:0.598750:0.000000 Dom v:@0.326637:0.614738:0.375590:0.614738:0.375590:0.598269:0.326637:0.598269:0.000000:0.000000:0.000000:0.000000:0.000000 ( ) = . En la figura 3.10. se mues-:@0.361854:0.614622:0.595755:0.614622:0.595755:0.598124:0.361854:0.598124:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.399018:0.613653:0.412927:0.613653:0.412927:0.600207:0.399018:0.600207:0.000000 tran las gráficas de las funciones y las cuales se cortan en un :@0.131674:0.642282:0.599952:0.642282:0.599952:0.625784:0.131674:0.625784:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u v,:@0.368440:0.642398:0.405179:0.642398:0.405179:0.625929:0.368440:0.625929:0.000000:0.000000:0.000000:0.000000 punto. Nótese que 2:@0.131674:0.667701:0.301808:0.666439:0.301808:0.649942:0.131674:0.651203:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.303206:0.666555:0.310681:0.666555:0.310681:0.650086:0.303206:0.650086:0.000000 −:@0.314091:0.667075:0.324667:0.667075:0.324667:0.650795:0.314091:0.650795:0.000000 3 está bien definido, si :@0.327392:0.666439:0.543269:0.667697:0.543269:0.651199:0.327392:0.649942:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x x:@0.508494:0.667812:0.526416:0.667585:0.526416:0.651116:0.508494:0.651344:0.000000:0.000000:0.000000 :@0.523079:0.667480:0.539127:0.667480:0.539127:0.652833:0.523079:0.652833:0.000000 ∈:@0.530154:0.668105:0.543890:0.668105:0.543890:0.651824:0.530154:0.651824:0.000000 ∞:@0.572094:0.668105:0.585830:0.668105:0.585830:0.651824:0.572094:0.651824:0.000000 3:@0.553812:0.658157:0.562308:0.658157:0.562308:0.641660:0.553812:0.641660:0.000000 2:@0.553600:0.678472:0.562096:0.678472:0.562096:0.661975:0.553600:0.661975:0.000000 ,:@0.566064:0.667469:0.568819:0.667469:0.568819:0.650971:0.566064:0.650971:0.000000 . , :@0.596214:0.667469:0.599908:0.667697:0.599908:0.651199:0.596214:0.650971:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y :@0.131685:0.694475:0.147790:0.694475:0.147790:0.677977:0.131685:0.677977:0.000000:0.000000:0.000000 2:@0.163251:0.694230:0.171671:0.694230:0.171671:0.677880:0.163251:0.677880:0.000000 3 0,:@0.195423:0.694230:0.234526:0.694230:0.234526:0.677880:0.195423:0.677880:0.000000:0.000000:0.000000:0.000000 3:@0.289018:0.685392:0.297438:0.685392:0.297438:0.669041:0.289018:0.669041:0.000000 2:@0.288808:0.705568:0.297228:0.705568:0.297228:0.689218:0.288808:0.689218:0.000000 ,:@0.301467:0.694233:0.304197:0.694233:0.304197:0.677883:0.301467:0.677883:0.000000 .:@0.328293:0.694233:0.331023:0.694233:0.331023:0.677883:0.328293:0.677883:0.000000 x:@0.173046:0.694348:0.180454:0.694348:0.180454:0.678026:0.173046:0.678026:0.000000 x:@0.252378:0.694348:0.259786:0.694348:0.259786:0.678026:0.252378:0.678026:0.000000 −≥:@0.183227:0.694861:0.218721:0.694861:0.218721:0.678726:0.183227:0.678726:0.000000:0.000000 ∈:@0.264114:0.694861:0.277728:0.694861:0.277728:0.678726:0.264114:0.678726:0.000000 ∞:@0.306807:0.694861:0.320420:0.694861:0.320420:0.678726:0.306807:0.678726:0.000000 :@0.237868:0.694477:0.277959:0.694477:0.277959:0.677979:0.237868:0.677979:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x x:@0.246152:0.694593:0.258179:0.694365:0.258179:0.677896:0.246152:0.678124:0.000000:0.000000:0.000000 :@0.257769:0.694260:0.273817:0.694260:0.273817:0.679613:0.257769:0.679613:0.000000 ∈:@0.261916:0.694886:0.275652:0.694886:0.275652:0.678605:0.261916:0.678605:0.000000 ∞:@0.303857:0.694886:0.317593:0.694886:0.317593:0.678605:0.303857:0.678605:0.000000 3:@0.285574:0.684938:0.294070:0.684938:0.294070:0.668440:0.285574:0.668440:0.000000 2:@0.285362:0.705253:0.293858:0.705253:0.293858:0.688755:0.285362:0.688755:0.000000 ,:@0.297827:0.694250:0.300582:0.694250:0.300582:0.677752:0.297827:0.677752:0.000000 . .:@0.327977:0.694250:0.327528:0.694477:0.327528:0.677979:0.327977:0.677752:0.000000:0.000000:0.000000 :@0.108232:0.729641:0.112374:0.729641:0.112374:0.713144:0.108232:0.713144:0.000000 Además, :@0.131685:0.729641:0.197409:0.729641:0.197409:0.713144:0.131685:0.713144:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.205620:0.728501:0.213095:0.728501:0.213095:0.712032:0.205620:0.712032:0.000000 −≥:@0.216505:0.729021:0.249641:0.729021:0.249641:0.712741:0.216505:0.712741:0.000000:0.000000 1:@0.229008:0.728385:0.237504:0.728385:0.237504:0.711888:0.229008:0.711888:0.000000 1:@0.254823:0.719074:0.263319:0.719074:0.263319:0.702576:0.254823:0.702576:0.000000 2:@0.254202:0.739387:0.262698:0.739387:0.262698:0.722889:0.254202:0.722889:0.000000 para :@0.267238:0.729643:0.335977:0.729643:0.335977:0.713145:0.267238:0.713145:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x x:@0.324360:0.729758:0.345353:0.729531:0.345353:0.713062:0.324360:0.713289:0.000000:0.000000:0.000000 :@0.340466:0.729426:0.356514:0.729426:0.356514:0.714779:0.340466:0.714779:0.000000 :@0.356514:0.729643:0.360656:0.729643:0.360656:0.713145:0.356514:0.713145:0.000000 ∈:@0.349091:0.730051:0.362827:0.730051:0.362827:0.713770:0.349091:0.713770:0.000000 ∞:@0.391031:0.730051:0.404767:0.730051:0.404767:0.713770:0.391031:0.713770:0.000000 3:@0.372748:0.720103:0.381244:0.720103:0.381244:0.703606:0.372748:0.703606:0.000000 2:@0.372536:0.740418:0.381032:0.740418:0.381032:0.723921:0.372536:0.723921:0.000000 ,:@0.385001:0.729415:0.387756:0.729415:0.387756:0.712917:0.385001:0.712917:0.000000 . , por lo que la igualdad :@0.415151:0.729415:0.599916:0.729643:0.599916:0.713145:0.415151:0.712917:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.157180:0.755173:0.164655:0.755173:0.164655:0.738705:0.157180:0.738705:0.000000 x:@0.208484:0.755173:0.215959:0.755173:0.215959:0.738705:0.208484:0.738705:0.000000 −:@0.168065:0.755694:0.127338:0.755694:0.127338:0.739413:0.168065:0.739413:0.000000 −:@0.219368:0.755694:0.178642:0.755694:0.178642:0.739413:0.219368:0.739413:0.000000 2:@0.147285:0.755058:0.155781:0.755058:0.155781:0.738560:0.147285:0.738560:0.000000 3 =:@0.181365:0.755058:0.204895:0.755058:0.204895:0.738560:0.181365:0.738560:0.000000:0.000000:0.000000 1 es compatible en el conjunto :@0.231886:0.755058:0.461273:0.755058:0.461273:0.738560:0.231886:0.738560:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.434019:0.754946:0.441494:0.754946:0.441494:0.738477:0.434019:0.738477:0.000000 ∈:@0.445231:0.755466:0.458967:0.755466:0.458967:0.739185:0.445231:0.739185:0.000000 ∞:@0.487171:0.755466:0.500908:0.755466:0.500908:0.739185:0.487171:0.739185:0.000000 3:@0.468889:0.745519:0.477385:0.745519:0.477385:0.729021:0.468889:0.729021:0.000000 2:@0.468677:0.765833:0.477173:0.765833:0.477173:0.749336:0.468677:0.749336:0.000000 ,:@0.481141:0.754830:0.483896:0.754830:0.483896:0.738332:0.481141:0.738332:0.000000 . . :@0.511292:0.754830:0.519127:0.755058:0.519127:0.738560:0.511292:0.738332:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.108238:0.783093:0.112380:0.783093:0.112380:0.766595:0.108238:0.766595:0.000000 ¿Tiene solución esta ecuación? Para dar respuesta a esta pregunta, :@0.131683:0.783093:0.599925:0.783093:0.599925:0.766595:0.131683:0.766595:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 elevamos al cuadrado ambos miembros :@0.131683:0.809871:0.442931:0.809871:0.442931:0.793373:0.131683:0.793373:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.471242:0.807366:0.479738:0.807366:0.479738:0.790869:0.471242:0.790869:0.000000 x:@0.481145:0.807482:0.488620:0.807482:0.488620:0.791013:0.481145:0.791013:0.000000 3:@0.503700:0.807366:0.512196:0.807366:0.512196:0.790869:0.503700:0.790869:0.000000 (:@0.451505:0.814762:0.395520:0.814762:0.395520:0.785456:0.451505:0.785456:0.000000 ):@0.513905:0.814762:0.457920:0.814762:0.457920:0.785456:0.513905:0.785456:0.000000 2:@0.520608:0.794143:0.525526:0.794143:0.525526:0.784594:0.520608:0.784594:0.000000 =:@0.530241:0.808003:0.540818:0.808003:0.540818:0.791722:0.530241:0.791722:0.000000 (:@0.543380:0.807366:0.549333:0.807366:0.549333:0.790869:0.543380:0.790869:0.000000 x:@0.550084:0.807482:0.557559:0.807482:0.557559:0.791013:0.550084:0.791013:0.000000 1):@0.571861:0.807366:0.584152:0.807366:0.584152:0.790869:0.571861:0.790869:0.000000:0.000000 2:@0.584477:0.799329:0.589394:0.799329:0.589394:0.789781:0.584477:0.789781:0.000000 , :@0.593011:0.809881:0.599908:0.809881:0.599908:0.793383:0.593011:0.793383:0.000000:0.000000 :@0.595765:0.809881:0.599908:0.809881:0.599908:0.793383:0.595765:0.793383:0.000000 de donde 2 – 3 = – 2 +1, con lo que ( – 2) = 0. :@0.131685:0.832509:0.510513:0.832512:0.510513:0.816015:0.131685:0.816012:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.213215:0.832625:0.220690:0.832625:0.220690:0.816156:0.213215:0.816156:0.000000 x:@0.267062:0.832625:0.274537:0.832625:0.274537:0.816156:0.267062:0.816156:0.000000 2:@0.274532:0.826159:0.279486:0.826159:0.279486:0.816541:0.274532:0.816541:0.000000 x:@0.306766:0.832628:0.314241:0.832628:0.314241:0.816159:0.306766:0.816159:0.000000 x:@0.430372:0.832628:0.437847:0.832628:0.437847:0.816159:0.430372:0.816159:0.000000 2:@0.471075:0.826159:0.476028:0.826159:0.476028:0.816541:0.471075:0.816541:0.000000 :@0.108236:0.868731:0.112378:0.868731:0.112378:0.852234:0.108236:0.852234:0.000000 La solución :@0.131681:0.868731:0.216639:0.868731:0.216639:0.852234:0.131681:0.852234:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 =:@0.233132:0.870621:0.243709:0.870621:0.243709:0.854340:0.233132:0.854340:0.000000 2:@0.246271:0.869985:0.254767:0.869985:0.254767:0.853487:0.246271:0.853487:0.000000 3:@0.283024:0.861144:0.291520:0.861144:0.291520:0.844646:0.283024:0.844646:0.000000 2:@0.282812:0.881343:0.291308:0.881343:0.291308:0.864845:0.282812:0.864845:0.000000 ,:@0.295222:0.869985:0.297977:0.869985:0.297977:0.853487:0.295222:0.853487:0.000000 ˆ:@0.223369:0.868339:0.231075:0.868339:0.231075:0.851842:0.223369:0.851842:0.000000 x:@0.223215:0.869641:0.230690:0.869641:0.230690:0.853172:0.223215:0.853172:0.000000 pertenece al conjunto. :@0.322183:0.868728:0.489635:0.868728:0.489635:0.852230:0.322183:0.852230:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.108222:0.897602:0.112365:0.897602:0.112365:0.881104:0.108222:0.881104:0.000000 Se verifica inmediatamente que :@0.131668:0.897602:0.364508:0.897602:0.364508:0.881104:0.131668:0.881104:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.379878:0.898482:0.388248:0.898482:0.388248:0.882230:0.379878:0.882230:0.000000 3:@0.413504:0.898482:0.421873:0.898482:0.421873:0.882230:0.413504:0.882230:0.000000 =:@0.425934:0.899109:0.436353:0.899109:0.436353:0.883070:0.425934:0.883070:0.000000 1:@0.463118:0.898482:0.471487:0.898482:0.471487:0.882230:0.463118:0.882230:0.000000 ˆ:@0.391149:0.897314:0.398740:0.897314:0.398740:0.881062:0.391149:0.881062:0.000000 x:@0.391000:0.898596:0.398364:0.898596:0.398364:0.882372:0.391000:0.882372:0.000000 ˆ:@0.441492:0.897322:0.449084:0.897322:0.449084:0.881069:0.441492:0.881069:0.000000 x:@0.441336:0.898596:0.448700:0.898596:0.448700:0.882372:0.441336:0.882372:0.000000 es la única solu-:@0.473432:0.897597:0.595782:0.897597:0.595782:0.881099:0.473432:0.881099:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ción del sistema.:@0.131686:0.914947:0.248007:0.914947:0.248007:0.898450:0.131686:0.898450:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.696388:0.673520:0.700096:0.673520:0.700096:0.666226:0.696388:0.666226:0.000000 –1:@0.641430:0.673520:0.649592:0.673520:0.649592:0.666226:0.641430:0.666226:0.000000:0.000000 2:@0.722758:0.673520:0.726466:0.673520:0.726466:0.666226:0.722758:0.666226:0.000000 3:@0.749127:0.673520:0.752836:0.673520:0.752836:0.666226:0.749127:0.666226:0.000000 4:@0.775497:0.673520:0.779206:0.673520:0.779206:0.666226:0.775497:0.666226:0.000000 5:@0.801867:0.673520:0.805575:0.673520:0.805575:0.666226:0.801867:0.666226:0.000000 6:@0.828237:0.673520:0.831945:0.673520:0.831945:0.666226:0.828237:0.666226:0.000000 1:@0.663505:0.647459:0.667214:0.647459:0.667214:0.640164:0.663505:0.640164:0.000000 2:@0.663505:0.627668:0.667214:0.627668:0.667214:0.620373:0.663505:0.620373:0.000000 3:@0.663505:0.607877:0.667214:0.607877:0.667214:0.600582:0.663505:0.600582:0.000000 0:@0.665983:0.673514:0.669692:0.673514:0.669692:0.666219:0.665983:0.666219:0.000000 y:@0.663614:0.589512:0.667097:0.589512:0.667097:0.582217:0.663614:0.582217:0.000000 x:@0.845046:0.670724:0.848420:0.670724:0.848420:0.663430:0.845046:0.663430:0.000000 y =√2x –3:@0.774275:0.626028:0.805826:0.626028:0.805826:0.618734:0.774275:0.618734:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.710113:0.670726:0.713822:0.670726:0.713822:0.663432:0.710113:0.663432:0.000000 2:@0.709963:0.677009:0.713671:0.677009:0.713671:0.669715:0.709963:0.669715:0.000000 y = –x+1:@0.724683:0.680511:0.753062:0.680511:0.753062:0.673216:0.724683:0.673216:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.793223:0.701027:0.804704:0.701027:0.804704:0.691003:0.793223:0.691003:0.000000 :@0.804704:0.701735:0.807585:0.701735:0.807585:0.690258:0.804704:0.690258:0.000000 Figura 3.9.:@0.807585:0.701735:0.856154:0.701735:0.856154:0.690258:0.807585:0.690258:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.698187:0.880765:0.701810:0.880765:0.701810:0.873640:0.698187:0.873640:0.000000 –1:@0.644502:0.880765:0.652475:0.880765:0.652475:0.873640:0.644502:0.873640:0.000000:0.000000 2:@0.723946:0.880765:0.727569:0.880765:0.727569:0.873640:0.723946:0.873640:0.000000 3:@0.749705:0.880765:0.753328:0.880765:0.753328:0.873640:0.749705:0.873640:0.000000 4:@0.775465:0.880765:0.779087:0.880765:0.779087:0.873640:0.775465:0.873640:0.000000 5:@0.801224:0.880765:0.804846:0.880765:0.804846:0.873640:0.801224:0.873640:0.000000 6:@0.826983:0.880765:0.830606:0.880765:0.830606:0.873640:0.826983:0.873640:0.000000 1:@0.666066:0.855307:0.669688:0.855307:0.669688:0.848182:0.666066:0.848182:0.000000 2:@0.666066:0.835975:0.669688:0.835975:0.669688:0.828849:0.666066:0.828849:0.000000 3:@0.666066:0.816642:0.669688:0.816642:0.669688:0.809516:0.666066:0.809516:0.000000 0:@0.668486:0.880759:0.672109:0.880759:0.672109:0.873634:0.668486:0.873634:0.000000 y:@0.666172:0.798702:0.669574:0.798702:0.669574:0.791577:0.666172:0.791577:0.000000 x:@0.844311:0.878034:0.847607:0.878034:0.847607:0.870909:0.844311:0.870909:0.000000 y =√2x –3:@0.783299:0.832347:0.814120:0.832347:0.814120:0.825222:0.783299:0.825222:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.711596:0.878037:0.715218:0.878037:0.715218:0.870912:0.711596:0.870912:0.000000 2:@0.711449:0.884174:0.715071:0.884174:0.715071:0.877049:0.711449:0.877049:0.000000 y = x+1:@0.747032:0.817573:0.770403:0.817573:0.770403:0.810448:0.747032:0.810448:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 –1:@0.661762:0.894405:0.669736:0.894405:0.669736:0.887279:0.661762:0.887279:0.000000:0.000000 p:@0.787313:0.922766:0.798794:0.922766:0.798794:0.912741:0.787313:0.912741:0.000000 Figura 3.10.:@0.798794:0.923474:0.856154:0.923474:0.856154:0.911997:0.798794:0.911997:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Competencia :@0.684804:0.104916:0.782426:0.104916:0.782426:0.089444:0.684804:0.089444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática:@0.684804:0.117484:0.768866:0.117484:0.768866:0.102012:0.684804:0.102012:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Tenemos la ecua-:@0.685042:0.141959:0.795206:0.141959:0.795206:0.126896:0.685042:0.126896:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ción :@0.638498:0.162197:0.669791:0.162197:0.669791:0.147134:0.638498:0.147134:0.000000:0.000000:0.000000:0.000000:0.000000 +=:@0.705500:0.163158:0.743414:0.163158:0.743414:0.146877:0.705500:0.146877:0.000000:0.000000 +:@0.765029:0.163158:0.775606:0.163158:0.775606:0.146877:0.765029:0.146877:0.000000 ,:@0.789419:0.162522:0.792174:0.162522:0.792174:0.146024:0.789419:0.146024:0.000000 ax bcxd:@0.685810:0.162638:0.787905:0.162638:0.787905:0.146169:0.685810:0.146169:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.795440:0.162201:0.799222:0.162201:0.799222:0.147138:0.795440:0.147138:0.000000 donde , , , con :@0.638502:0.178043:0.818429:0.178043:0.818429:0.162980:0.638502:0.162980:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b c d:@0.688880:0.178149:0.739363:0.178149:0.739363:0.163112:0.688880:0.163112:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.743145:0.177845:0.757797:0.177845:0.757797:0.164472:0.743145:0.164472:0.000000 R:@0.761578:0.177159:0.774278:0.177159:0.774278:0.164881:0.761578:0.164881:0.000000 a:@0.806450:0.178149:0.814647:0.178149:0.814647:0.163112:0.806450:0.163112:0.000000 ≠0, ≠ 0. Sean , las fun-:@0.638501:0.193885:0.811638:0.193885:0.811638:0.178822:0.638501:0.178822:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 c:@0.662423:0.193991:0.668984:0.193991:0.668984:0.178954:0.662423:0.178954:0.000000 u v:@0.738764:0.193991:0.760576:0.193991:0.760576:0.178954:0.738764:0.178954:0.000000:0.000000:0.000000 ciones reales definidas por :@0.638501:0.209727:0.812973:0.209727:0.812973:0.194664:0.638501:0.194664:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ux:@0.640651:0.230406:0.663981:0.230406:0.663981:0.213937:0.640651:0.213937:0.000000:0.000000 ax bv x:@0.701529:0.230406:0.773812:0.230406:0.773812:0.213937:0.701529:0.213937:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cxd:@0.798318:0.230406:0.838486:0.230406:0.838486:0.213937:0.798318:0.213937:0.000000:0.000000:0.000000 ():@0.649811:0.230290:0.670367:0.230290:0.670367:0.213793:0.649811:0.213793:0.000000:0.000000 ,( ):@0.745926:0.230290:0.780204:0.230290:0.780204:0.213793:0.745926:0.213793:0.000000:0.000000:0.000000:0.000000 ,:@0.840004:0.230290:0.842759:0.230290:0.842759:0.213793:0.840004:0.213793:0.000000 =:@0.673841:0.230927:0.684418:0.230927:0.684418:0.214646:0.673841:0.214646:0.000000 +:@0.721002:0.230927:0.731579:0.230927:0.731579:0.214646:0.721002:0.214646:0.000000 =:@0.783675:0.230927:0.794251:0.230927:0.794251:0.214646:0.783675:0.214646:0.000000 +:@0.815828:0.230927:0.826405:0.230927:0.826405:0.214646:0.815828:0.214646:0.000000 entonces :@0.638503:0.251682:0.701368:0.251682:0.701368:0.236619:0.638503:0.236619:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 {:@0.710644:0.273114:0.719892:0.273114:0.719892:0.250484:0.710644:0.250484:0.000000 }:@0.837487:0.273114:0.846734:0.273114:0.846734:0.250484:0.837487:0.250484:0.000000 ∈:@0.732161:0.270367:0.745897:0.270367:0.745897:0.254086:0.732161:0.254086:0.000000 + ≥:@0.788916:0.270367:0.825289:0.270367:0.825289:0.254086:0.788916:0.254086:0.000000:0.000000:0.000000 ()=:@0.675040:0.269731:0.708561:0.269731:0.708561:0.253233:0.675040:0.253233:0.000000:0.000000:0.000000 |:@0.761945:0.269731:0.766954:0.269731:0.766954:0.253233:0.761945:0.253233:0.000000 0,:@0.828801:0.269731:0.851245:0.269731:0.851245:0.253233:0.828801:0.253233:0.000000:0.000000 Domu:@0.641070:0.269846:0.689387:0.269846:0.689387:0.253378:0.641070:0.253378:0.000000:0.000000:0.000000:0.000000 x:@0.720905:0.269846:0.728380:0.269846:0.728380:0.253378:0.720905:0.253378:0.000000 axb:@0.769222:0.269846:0.811471:0.269846:0.811471:0.253378:0.769222:0.253378:0.000000:0.000000:0.000000 () =:@0.679495:0.294586:0.712188:0.294586:0.712188:0.278089:0.679495:0.278089:0.000000:0.000000:0.000000:0.000000 Domv:@0.645530:0.294702:0.692422:0.294702:0.692422:0.278233:0.645530:0.278233:0.000000:0.000000:0.000000:0.000000 .:@0.732317:0.294266:0.734832:0.294266:0.734832:0.279203:0.732317:0.279203:0.000000 Si ( )≥0 para :@0.638509:0.317237:0.731578:0.317237:0.731578:0.302173:0.638509:0.302173:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 v x:@0.653074:0.317342:0.672440:0.317342:0.672440:0.302305:0.653074:0.302305:0.000000:0.000000:0.000000 x :@0.731578:0.317342:0.742185:0.317342:0.742185:0.302305:0.731578:0.302305:0.000000:0.000000  :@0.742185:0.317039:0.761235:0.317039:0.761235:0.303665:0.742185:0.303665:0.000000:0.000000 Dom u:@0.761235:0.317342:0.807233:0.317342:0.807233:0.302305:0.761235:0.302305:0.000000:0.000000:0.000000:0.000000:0.000000 ( ), la :@0.793389:0.317237:0.833389:0.317237:0.833389:0.302173:0.793389:0.302173:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 igualdad :@0.638509:0.338742:0.697541:0.338742:0.697541:0.323679:0.638509:0.323679:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 +:@0.733238:0.338435:0.685499:0.338435:0.685499:0.322154:0.733238:0.322154:0.000000 +:@0.791554:0.338435:0.743815:0.338435:0.743815:0.322154:0.791554:0.322154:0.000000 =:@0.760148:0.337798:0.770955:0.337798:0.770955:0.321301:0.760148:0.321301:0.000000 ax bcxd:@0.713564:0.337914:0.814441:0.337914:0.814441:0.321445:0.713564:0.321445:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 es :@0.818153:0.338735:0.842620:0.338735:0.842620:0.323672:0.818153:0.323672:0.000000:0.000000:0.000000:0.000000:0.000000 compatible para, al menos, un :@0.638506:0.354577:0.837832:0.354577:0.837832:0.339514:0.638506:0.339514:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 número real :@0.638506:0.370419:0.720968:0.370419:0.720968:0.355356:0.638506:0.355356:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.720968:0.370525:0.731575:0.370525:0.731575:0.355488:0.720968:0.355488:0.000000:0.000000  :@0.731575:0.370221:0.750625:0.370221:0.750625:0.356848:0.731575:0.356848:0.000000:0.000000 Dom u:@0.750625:0.370525:0.796623:0.370525:0.796623:0.355488:0.750625:0.355488:0.000000:0.000000:0.000000:0.000000:0.000000 ( ).:@0.782779:0.370419:0.804573:0.370419:0.804573:0.355356:0.782779:0.355356:0.000000:0.000000:0.000000:0.000000 En tal caso, resolvemos la :@0.638506:0.393390:0.805555:0.393390:0.805555:0.378327:0.638506:0.378327:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ecuación. Elevamos ambos :@0.638506:0.409232:0.816040:0.409232:0.816040:0.394169:0.638506:0.394169:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 miembros al cuadrado. Si el :@0.638506:0.425074:0.819805:0.425074:0.819805:0.410011:0.638506:0.410011:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 discriminante de esta ecuación :@0.638506:0.440916:0.842969:0.440916:0.842969:0.425853:0.638506:0.425853:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de segundo grado es negativo, :@0.638506:0.456758:0.838923:0.456758:0.838923:0.441695:0.638506:0.441695:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la ecuación :@0.638506:0.478263:0.715443:0.478263:0.715443:0.463200:0.638506:0.463200:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 +:@0.751145:0.477957:0.703406:0.477957:0.703406:0.461677:0.751145:0.461677:0.000000 +:@0.809461:0.477957:0.761721:0.477957:0.761721:0.461677:0.809461:0.461677:0.000000 =:@0.778054:0.477321:0.788862:0.477321:0.788862:0.460823:0.778054:0.460823:0.000000 ax bcxd:@0.731471:0.477437:0.832348:0.477437:0.832348:0.460968:0.731471:0.460968:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.836059:0.478258:0.839841:0.478258:0.839841:0.463195:0.836059:0.463195:0.000000 no tiene solución en .:@0.638506:0.494100:0.790078:0.494100:0.790078:0.479037:0.638506:0.479037:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.774863:0.493215:0.787563:0.493215:0.787563:0.480938:0.774863:0.480938:0.000000 ©:@0.079553:0.731952:0.079553:0.720342:0.061505:0.720342:0.061505:0.731952:0.000000:0.000000 maya:@0.080774:0.720340:0.080774:0.684191:0.055786:0.684191:0.055786:0.720340:0.000000:0.000000:0.000000:0.000000 ®EDUCACIÓN – Libro resuelto solo para fines didácticos – Prohibida su reproducción :@0.079553:0.684191:0.079553:0.268044:0.061505:0.268044:0.061505:0.684191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000