84:@0.036727:0.974518:0.057230:0.974518:0.057230:0.956333:0.036727:0.956333:0.000000:0.000000 Polinomios algebraicos:@0.073089:0.043661:0.280500:0.043661:0.280500:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 La suma de polinomios :@0.078581:0.184270:0.236047:0.184270:0.236047:0.169331:0.078581:0.169331:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 se puede hacer en forma :@0.078581:0.199399:0.246793:0.199399:0.246793:0.184460:0.078581:0.184460:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 vertical. Para ello, es :@0.078581:0.214528:0.211786:0.214528:0.211786:0.199589:0.078581:0.199589:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 recomendable ordenar :@0.078581:0.229657:0.234629:0.229657:0.234629:0.214717:0.078581:0.214717:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 en forma descendente y :@0.078581:0.244786:0.243038:0.244786:0.243038:0.229846:0.078581:0.229846:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 completar los polinomios.:@0.078581:0.259915:0.249795:0.259915:0.249795:0.244975:0.078581:0.244975:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Competencia :@0.078581:0.144831:0.187141:0.144831:0.187141:0.127884:0.078581:0.127884:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática :@0.078581:0.161472:0.176057:0.161472:0.176057:0.144526:0.078581:0.144526:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Al sumar polinomios, aplicamos la propiedad asociativa y conmutativa, de manera que :@0.301224:0.142792:0.923568:0.142792:0.923568:0.126358:0.301224:0.126358:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 reagrupamos términos semejantes para reducirlos.:@0.301224:0.159434:0.667952:0.159434:0.667952:0.143000:0.301224:0.143000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Ejemplo 3:@0.293658:0.198154:0.369441:0.198154:0.369441:0.181484:0.293658:0.181484:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Suma 2:@0.293658:0.234724:0.404897:0.234728:0.404897:0.218294:0.293658:0.218290:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.343181:0.228486:0.352163:0.228486:0.352163:0.212052:0.343181:0.212052:0.000000 2:@0.343181:0.242465:0.352163:0.242465:0.352163:0.226031:0.343181:0.226031:0.000000 x:@0.360189:0.234727:0.367644:0.234727:0.367644:0.218321:0.360189:0.218321:0.000000 3:@0.367569:0.228664:0.372805:0.228664:0.372805:0.219083:0.367569:0.219083:0.000000 1:@0.376715:0.234173:0.392049:0.234173:0.392049:0.220458:0.376715:0.220458:0.000000 x y:@0.404805:0.234728:0.424854:0.234728:0.424854:0.218322:0.404805:0.218322:0.000000:0.000000:0.000000 2:@0.412191:0.228664:0.417428:0.228664:0.417428:0.219083:0.412191:0.219083:0.000000 3 con :@0.424780:0.234728:0.505066:0.234728:0.505066:0.218294:0.424780:0.218294:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.428738:0.234173:0.444071:0.234173:0.444071:0.220458:0.428738:0.220458:0.000000 y:@0.456827:0.234728:0.464300:0.234728:0.464300:0.218322:0.456827:0.218322:0.000000 3:@0.464240:0.228664:0.469477:0.228664:0.469477:0.219083:0.464240:0.219083:0.000000 2:@0.504955:0.234173:0.520289:0.234173:0.520289:0.220458:0.504955:0.220458:0.000000 2:@0.524343:0.228486:0.533326:0.228486:0.533326:0.212052:0.524343:0.212052:0.000000 5:@0.524343:0.242465:0.533326:0.242465:0.533326:0.226031:0.524343:0.226031:0.000000 :@0.537394:0.234727:0.557951:0.234728:0.557951:0.218294:0.537394:0.218293:0.000000:0.000000:0.000000 x:@0.541351:0.234727:0.548806:0.234727:0.548806:0.218321:0.541351:0.218321:0.000000 3:@0.548731:0.228664:0.553968:0.228664:0.553968:0.219083:0.548731:0.219083:0.000000 2:@0.557878:0.234173:0.573211:0.234173:0.573211:0.220458:0.557878:0.220458:0.000000 1:@0.577257:0.228486:0.586240:0.228486:0.586240:0.212052:0.577257:0.212052:0.000000 4:@0.577257:0.242465:0.586240:0.242465:0.586240:0.226031:0.577257:0.226031:0.000000 :@0.590308:0.234727:0.594339:0.234727:0.594339:0.218293:0.590308:0.218293:0.000000 x y:@0.594266:0.234727:0.614308:0.234728:0.614308:0.218322:0.594266:0.218321:0.000000:0.000000:0.000000 2:@0.601645:0.228664:0.606882:0.228664:0.606882:0.219083:0.601645:0.219083:0.000000 3:@0.614234:0.234728:0.642416:0.234728:0.642416:0.218294:0.614234:0.218294:0.000000:0.000000:0.000000 2:@0.618192:0.234173:0.633525:0.234173:0.633525:0.220458:0.618192:0.220458:0.000000 xy:@0.642342:0.234728:0.657399:0.234728:0.657399:0.218322:0.642342:0.218322:0.000000:0.000000 2:@0.657334:0.228664:0.662571:0.228664:0.662571:0.219083:0.657334:0.219083:0.000000 4:@0.662525:0.234728:0.694664:0.234728:0.694664:0.218294:0.662525:0.218294:0.000000:0.000000:0.000000:0.000000 1:@0.666482:0.234173:0.681816:0.234173:0.681816:0.220458:0.666482:0.220458:0.000000 y:@0.694572:0.234728:0.702045:0.234728:0.702045:0.218322:0.694572:0.218322:0.000000 3:@0.701977:0.228664:0.707213:0.228664:0.707213:0.219083:0.701977:0.219083:0.000000 Solución:@0.293660:0.266737:0.359794:0.266737:0.359794:0.250068:0.293660:0.250068:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.297805:0.297066:0.306788:0.297066:0.306788:0.280632:0.297805:0.280632:0.000000 2:@0.297805:0.311045:0.306788:0.311045:0.306788:0.294611:0.297805:0.294611:0.000000 x:@0.310856:0.303306:0.318311:0.303306:0.318311:0.286900:0.310856:0.286900:0.000000 3:@0.318242:0.297244:0.323479:0.297244:0.323479:0.287663:0.318242:0.287663:0.000000 + 2:@0.323431:0.303308:0.351226:0.303308:0.351226:0.286874:0.323431:0.286874:0.000000:0.000000:0.000000:0.000000 x y:@0.351116:0.303308:0.371176:0.303308:0.371176:0.286901:0.351116:0.286901:0.000000:0.000000:0.000000 2:@0.358514:0.297244:0.363751:0.297244:0.363751:0.287663:0.358514:0.287663:0.000000 3 + :@0.371103:0.303308:0.430687:0.303308:0.430687:0.286874:0.371103:0.286874:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.375060:0.302753:0.390394:0.302753:0.390394:0.289037:0.375060:0.289037:0.000000 y:@0.399211:0.303308:0.406684:0.303308:0.406684:0.286901:0.399211:0.286901:0.000000 3:@0.406612:0.297244:0.411849:0.297244:0.411849:0.287663:0.406612:0.287663:0.000000 2:@0.433877:0.302753:0.449210:0.302753:0.449210:0.289037:0.433877:0.289037:0.000000 2:@0.451809:0.297066:0.460791:0.297066:0.460791:0.280632:0.451809:0.280632:0.000000 5:@0.451809:0.311045:0.460791:0.311045:0.460791:0.294611:0.451809:0.294611:0.000000 x :@0.463405:0.303306:0.480437:0.303308:0.480437:0.286874:0.463405:0.286872:0.000000:0.000000:0.000000 3:@0.471215:0.297244:0.476452:0.297244:0.476452:0.287663:0.471215:0.287663:0.000000 2:@0.480363:0.302753:0.495696:0.302753:0.495696:0.289037:0.480363:0.289037:0.000000 1:@0.498287:0.297066:0.507270:0.297066:0.507270:0.280632:0.498287:0.280632:0.000000 4:@0.498287:0.311045:0.507270:0.311045:0.507270:0.294611:0.498287:0.294611:0.000000 x y:@0.509883:0.303306:0.529931:0.303308:0.529931:0.286901:0.509883:0.286900:0.000000:0.000000:0.000000 2:@0.517266:0.297244:0.522503:0.297244:0.522503:0.287663:0.517266:0.287663:0.000000 3:@0.529857:0.303308:0.558038:0.303308:0.558038:0.286874:0.529857:0.286874:0.000000:0.000000:0.000000 2:@0.533815:0.302753:0.549148:0.302753:0.549148:0.289037:0.533815:0.289037:0.000000 xy:@0.557965:0.303308:0.573022:0.303308:0.573022:0.286901:0.557965:0.286901:0.000000:0.000000 2:@0.572957:0.297244:0.578194:0.297244:0.578194:0.287663:0.572957:0.287663:0.000000 4:@0.578146:0.303308:0.610285:0.303308:0.610285:0.286874:0.578146:0.286874:0.000000:0.000000:0.000000:0.000000 1:@0.582103:0.302753:0.597437:0.302753:0.597437:0.289037:0.582103:0.289037:0.000000 y:@0.610193:0.303308:0.617666:0.303308:0.617666:0.286901:0.610193:0.286901:0.000000 3:@0.617598:0.297244:0.622835:0.297244:0.622835:0.287663:0.617598:0.287663:0.000000 :@0.626072:0.303890:0.630674:0.303890:0.630674:0.286236:0.626072:0.286236:0.000000 Sumamos.:@0.630581:0.303308:0.706541:0.303308:0.706541:0.286874:0.630581:0.286874:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.297805:0.333636:0.306788:0.333636:0.306788:0.317202:0.297805:0.317202:0.000000 2:@0.297805:0.347615:0.306788:0.347615:0.306788:0.331181:0.297805:0.331181:0.000000 x:@0.310856:0.339877:0.318311:0.339877:0.318311:0.323471:0.310856:0.323471:0.000000 3:@0.318242:0.333814:0.323479:0.333814:0.323479:0.324233:0.318242:0.324233:0.000000 + 2:@0.323431:0.339878:0.351226:0.339878:0.351226:0.323444:0.323431:0.323444:0.000000:0.000000:0.000000:0.000000 x y:@0.351116:0.339878:0.371176:0.339878:0.371176:0.323472:0.351116:0.323472:0.000000:0.000000:0.000000 2:@0.358514:0.333814:0.363751:0.333814:0.363751:0.324233:0.358514:0.324233:0.000000 3 x :@0.371103:0.339878:0.466262:0.339878:0.466262:0.323444:0.371103:0.323444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.375060:0.339323:0.390394:0.339323:0.390394:0.325608:0.375060:0.325608:0.000000 y:@0.399211:0.339878:0.406684:0.339878:0.406684:0.323472:0.399211:0.323472:0.000000 3:@0.406612:0.333814:0.411849:0.333814:0.411849:0.324233:0.406612:0.324233:0.000000 2:@0.415759:0.339323:0.431092:0.339323:0.431092:0.325608:0.415759:0.325608:0.000000 2:@0.437633:0.333636:0.446616:0.333636:0.446616:0.317202:0.437633:0.317202:0.000000 5:@0.437633:0.347615:0.446616:0.347615:0.446616:0.331181:0.437633:0.331181:0.000000 3:@0.457041:0.333814:0.462278:0.333814:0.462278:0.324233:0.457041:0.324233:0.000000 2:@0.466188:0.339323:0.481521:0.339323:0.481521:0.325608:0.466188:0.325608:0.000000 1:@0.484112:0.333636:0.493094:0.333636:0.493094:0.317202:0.484112:0.317202:0.000000 4:@0.484112:0.347615:0.493094:0.347615:0.493094:0.331181:0.484112:0.331181:0.000000 x y:@0.495708:0.339877:0.515755:0.339878:0.515755:0.323472:0.495708:0.323471:0.000000:0.000000:0.000000 2:@0.503093:0.333814:0.508330:0.333814:0.508330:0.324233:0.503093:0.324233:0.000000 3:@0.515682:0.339878:0.543863:0.339878:0.543863:0.323444:0.515682:0.323444:0.000000:0.000000:0.000000 2:@0.519639:0.339323:0.534973:0.339323:0.534973:0.325608:0.519639:0.325608:0.000000 xy:@0.543790:0.339878:0.558847:0.339878:0.558847:0.323472:0.543790:0.323472:0.000000:0.000000 2:@0.558781:0.333814:0.564018:0.333814:0.564018:0.324233:0.558781:0.324233:0.000000 4 Destruimos el parénteis.:@0.563971:0.339878:0.782143:0.339878:0.782143:0.323444:0.563971:0.323444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.567928:0.339323:0.583261:0.339323:0.583261:0.325608:0.567928:0.325608:0.000000 y:@0.596018:0.339878:0.603491:0.339878:0.603491:0.323472:0.596018:0.323472:0.000000 :@0.603417:0.340460:0.608019:0.340460:0.608019:0.322806:0.603417:0.322806:0.000000 Aplicamos las propiedades asociativa y conmutativa.:@0.293660:0.371886:0.674444:0.371886:0.674444:0.355452:0.293660:0.355452:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.299634:0.402217:0.308617:0.402217:0.308617:0.385783:0.299634:0.385783:0.000000 2:@0.299634:0.416196:0.308617:0.416196:0.308617:0.399762:0.299634:0.399762:0.000000 x:@0.311231:0.408457:0.318686:0.408457:0.318686:0.392051:0.311231:0.392051:0.000000 3:@0.318614:0.402394:0.323851:0.402394:0.323851:0.392813:0.318614:0.392813:0.000000 :@0.323805:0.408457:0.327836:0.408457:0.327836:0.392024:0.323805:0.392024:0.000000 2:@0.327762:0.407903:0.343095:0.407903:0.343095:0.394187:0.327762:0.394187:0.000000 2:@0.345686:0.402217:0.354668:0.402217:0.354668:0.385783:0.345686:0.385783:0.000000 5:@0.345686:0.416196:0.354668:0.416196:0.354668:0.399762:0.345686:0.399762:0.000000 x:@0.357282:0.408457:0.364737:0.408457:0.364737:0.392051:0.357282:0.392051:0.000000 3:@0.364665:0.402394:0.369902:0.402394:0.369902:0.392813:0.364665:0.392813:0.000000 :@0.373139:0.409040:0.397492:0.409040:0.397492:0.391386:0.373139:0.391386:0.000000:0.000000:0.000000 1:@0.377649:0.407903:0.392982:0.407903:0.392982:0.394187:0.377649:0.394187:0.000000 2 y :@0.400685:0.408457:0.434223:0.408457:0.434223:0.392024:0.400685:0.392024:0.000000:0.000000:0.000000:0.000000 x:@0.409587:0.408457:0.417042:0.408457:0.417042:0.392051:0.409587:0.392051:0.000000 2:@0.416975:0.402394:0.422212:0.402394:0.422212:0.392813:0.416975:0.392813:0.000000 2:@0.434131:0.407903:0.449464:0.407903:0.449464:0.394187:0.434131:0.394187:0.000000 1:@0.452066:0.402217:0.461049:0.402217:0.461049:0.385783:0.452066:0.385783:0.000000 4:@0.452066:0.416196:0.461049:0.416196:0.461049:0.399762:0.452066:0.399762:0.000000 x y:@0.463663:0.408457:0.483708:0.408457:0.483708:0.392051:0.463663:0.392051:0.000000:0.000000:0.000000 2:@0.471046:0.402394:0.476283:0.402394:0.476283:0.392813:0.471046:0.392813:0.000000 :@0.486928:0.409040:0.491530:0.409040:0.491530:0.391386:0.486928:0.391386:0.000000 2:@0.491438:0.407903:0.506771:0.407903:0.506771:0.394187:0.491438:0.394187:0.000000 3:@0.506679:0.408457:0.515662:0.408457:0.515662:0.392024:0.506679:0.392024:0.000000 xy:@0.515588:0.408457:0.530645:0.408457:0.530645:0.392051:0.515588:0.392051:0.000000:0.000000 2:@0.530578:0.402394:0.535815:0.402394:0.535815:0.392813:0.530578:0.392813:0.000000 :@0.535769:0.408457:0.539800:0.408457:0.539800:0.392024:0.535769:0.392024:0.000000 1 2:@0.539727:0.407903:0.578087:0.407903:0.578087:0.394187:0.539727:0.394187:0.000000:0.000000:0.000000:0.000000 3 4:@0.577995:0.408457:0.631634:0.408457:0.631634:0.392024:0.577995:0.392024:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.586904:0.408457:0.594378:0.408457:0.594378:0.392051:0.586904:0.392051:0.000000 3:@0.594304:0.402394:0.599541:0.402394:0.599541:0.392813:0.594304:0.392813:0.000000 1:@0.603453:0.407903:0.618786:0.407903:0.618786:0.394187:0.603453:0.394187:0.000000 y:@0.631542:0.408457:0.639015:0.408457:0.639015:0.392051:0.631542:0.392051:0.000000 3:@0.638947:0.402394:0.644184:0.402394:0.644184:0.392813:0.638947:0.392813:0.000000 1:@0.300553:0.438787:0.309536:0.438787:0.309536:0.422353:0.300553:0.422353:0.000000 10:@0.296098:0.452766:0.313990:0.452766:0.313990:0.436333:0.296098:0.436333:0.000000:0.000000 x:@0.316346:0.445028:0.323801:0.445028:0.323801:0.428622:0.316346:0.428622:0.000000 3:@0.323736:0.438964:0.328973:0.438964:0.328973:0.429383:0.323736:0.429383:0.000000 :@0.328927:0.445028:0.332958:0.445028:0.332958:0.428594:0.328927:0.428594:0.000000 1:@0.332884:0.444473:0.348218:0.444473:0.348218:0.430757:0.332884:0.430757:0.000000 7:@0.350808:0.438787:0.359791:0.438787:0.359791:0.422353:0.350808:0.422353:0.000000 4:@0.350808:0.452766:0.359791:0.452766:0.359791:0.436333:0.350808:0.436333:0.000000 x y:@0.362405:0.445028:0.382452:0.445028:0.382452:0.428622:0.362405:0.428622:0.000000:0.000000:0.000000 2:@0.369788:0.438964:0.375024:0.438964:0.375024:0.429383:0.369788:0.429383:0.000000 3:@0.382378:0.445028:0.410560:0.445028:0.410560:0.428594:0.382378:0.428594:0.000000:0.000000:0.000000 2:@0.386336:0.444473:0.401669:0.444473:0.401669:0.430757:0.386336:0.430757:0.000000 xy:@0.410486:0.445028:0.425543:0.445028:0.425543:0.428622:0.410486:0.428622:0.000000:0.000000 2:@0.425476:0.438964:0.430713:0.438964:0.430713:0.429383:0.425476:0.429383:0.000000 Reducimos términos semejantes.:@0.430667:0.445028:0.709991:0.445028:0.709991:0.428594:0.430667:0.428594:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.434625:0.444473:0.449958:0.444473:0.449958:0.430757:0.434625:0.430757:0.000000 y:@0.453823:0.445028:0.461297:0.445028:0.461297:0.428622:0.453823:0.428622:0.000000 3:@0.461216:0.438964:0.466453:0.438964:0.466453:0.429383:0.461216:0.429383:0.000000 Ejemplo 4:@0.293653:0.477036:0.369436:0.477036:0.369436:0.460366:0.293653:0.460366:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 De la suma del polinomio con el polinomio , resta el polinomio .:@0.293653:0.509043:0.801916:0.509046:0.801916:0.492612:0.293653:0.492610:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 P:@0.484003:0.509043:0.492765:0.509043:0.492765:0.492637:0.484003:0.492637:0.000000 1:@0.492696:0.512218:0.497933:0.512218:0.497933:0.502637:0.492696:0.502637:0.000000 P:@0.629331:0.509046:0.638093:0.509046:0.638093:0.492640:0.629331:0.492640:0.000000 3:@0.638030:0.512218:0.643267:0.512218:0.643267:0.502637:0.638030:0.502637:0.000000 P:@0.784828:0.509046:0.793589:0.509046:0.793589:0.492640:0.784828:0.492640:0.000000 2:@0.793522:0.512218:0.798759:0.512218:0.798759:0.502637:0.793522:0.502637:0.000000 P : 4 3 :@0.293655:0.541054:0.408016:0.541055:0.408016:0.524621:0.293655:0.524620:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.302819:0.544227:0.308055:0.544227:0.308055:0.534646:0.302819:0.534646:0.000000 2:@0.319035:0.540500:0.334369:0.540500:0.334369:0.526785:0.319035:0.526785:0.000000 a:@0.343186:0.541055:0.352445:0.541055:0.352445:0.524649:0.343186:0.524649:0.000000 4:@0.352369:0.534991:0.357606:0.534991:0.357606:0.525410:0.352369:0.525410:0.000000 2:@0.361516:0.540500:0.376849:0.540500:0.376849:0.526785:0.361516:0.526785:0.000000 a:@0.389605:0.541055:0.398864:0.541055:0.398864:0.524649:0.389605:0.524649:0.000000 2:@0.398796:0.534991:0.404033:0.534991:0.404033:0.525410:0.398796:0.525410:0.000000 2 1:@0.407942:0.540500:0.451660:0.540500:0.451660:0.526785:0.407942:0.526785:0.000000:0.000000:0.000000 a:@0.423184:0.541055:0.432442:0.541055:0.432442:0.524649:0.423184:0.524649:0.000000 1:@0.432369:0.541055:0.464508:0.541055:0.464508:0.524621:0.432369:0.524621:0.000000:0.000000:0.000000:0.000000 P : 2:@0.293670:0.576294:0.324079:0.576289:0.324079:0.559855:0.293670:0.559860:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.302819:0.579461:0.308055:0.579461:0.308055:0.569880:0.302819:0.569880:0.000000 a:@0.323987:0.576289:0.333246:0.576289:0.333246:0.559883:0.323987:0.559883:0.000000 5:@0.333177:0.570225:0.338414:0.570225:0.338414:0.560644:0.333177:0.560644:0.000000 :@0.338366:0.576872:0.362719:0.576872:0.362719:0.559217:0.338366:0.559217:0.000000:0.000000:0.000000 2:@0.342876:0.575734:0.358209:0.575734:0.358209:0.562019:0.342876:0.562019:0.000000 a:@0.365912:0.576289:0.375171:0.576289:0.375171:0.559883:0.365912:0.559883:0.000000 4:@0.375104:0.570225:0.380341:0.570225:0.380341:0.560644:0.375104:0.560644:0.000000 :@0.380295:0.576289:0.384326:0.576289:0.384326:0.559855:0.380295:0.559855:0.000000 2:@0.384252:0.575734:0.399586:0.575734:0.399586:0.562019:0.384252:0.562019:0.000000 :@0.399493:0.576872:0.404095:0.576872:0.404095:0.559217:0.399493:0.559217:0.000000 7 1:@0.407280:0.576289:0.462704:0.576289:0.462704:0.559855:0.407280:0.559855:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.416182:0.576289:0.425441:0.576289:0.425441:0.559883:0.416182:0.559883:0.000000 2:@0.425376:0.570225:0.430613:0.570225:0.430613:0.560644:0.425376:0.560644:0.000000 1:@0.434522:0.575734:0.449856:0.575734:0.449856:0.562019:0.434522:0.562019:0.000000 :@0.465893:0.576872:0.470495:0.576872:0.470495:0.559217:0.465893:0.559217:0.000000 2:@0.470403:0.575734:0.485736:0.575734:0.485736:0.562019:0.470403:0.562019:0.000000 3:@0.485644:0.576289:0.494627:0.576289:0.494627:0.559855:0.485644:0.559855:0.000000 a:@0.494554:0.576289:0.503812:0.576289:0.503812:0.559883:0.494554:0.559883:0.000000 3:@0.503740:0.570225:0.508977:0.570225:0.508977:0.560644:0.503740:0.560644:0.000000 P : 10 8 3:@0.293660:0.608298:0.421877:0.608298:0.421877:0.591864:0.293660:0.591864:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.302819:0.611470:0.308055:0.611470:0.308055:0.601890:0.302819:0.601890:0.000000 a:@0.332878:0.608298:0.342136:0.608298:0.342136:0.591892:0.332878:0.591892:0.000000 4:@0.342080:0.602234:0.347316:0.602234:0.347316:0.592653:0.342080:0.592653:0.000000 2:@0.351226:0.607743:0.366560:0.607743:0.366560:0.594028:0.351226:0.594028:0.000000 a:@0.379316:0.608298:0.388575:0.608298:0.388575:0.591892:0.379316:0.591892:0.000000 3:@0.388506:0.602234:0.393743:0.602234:0.393743:0.592653:0.388506:0.592653:0.000000 2:@0.397653:0.607743:0.412986:0.607743:0.412986:0.594028:0.397653:0.594028:0.000000 a:@0.421803:0.608298:0.431062:0.608298:0.431062:0.591892:0.421803:0.591892:0.000000 2:@0.430982:0.602234:0.436218:0.602234:0.436218:0.592653:0.430982:0.592653:0.000000 Solución:@0.293660:0.640307:0.359794:0.640307:0.359794:0.623638:0.293660:0.623638:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Sumamos los polinomios P y P ::@0.293660:0.672315:0.528706:0.672316:0.528706:0.655882:0.293660:0.655881:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.490044:0.675489:0.495281:0.675489:0.495281:0.665908:0.490044:0.665908:0.000000 3:@0.520314:0.675489:0.525551:0.675489:0.525551:0.665908:0.520314:0.665908:0.000000 2:@0.296031:0.702090:0.311365:0.702090:0.311365:0.688374:0.296031:0.688374:0.000000 4 :@0.311273:0.702645:0.384239:0.702645:0.384239:0.686211:0.311273:0.686211:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.320182:0.702645:0.329440:0.702645:0.329440:0.686239:0.320182:0.686239:0.000000 4:@0.329367:0.696581:0.334604:0.696581:0.334604:0.687000:0.329367:0.687000:0.000000 2:@0.389296:0.702090:0.404629:0.702090:0.404629:0.688374:0.389296:0.688374:0.000000 3:@0.404537:0.702645:0.413520:0.702645:0.413520:0.686211:0.404537:0.686211:0.000000 a:@0.413446:0.702645:0.422705:0.702645:0.422705:0.686239:0.413446:0.686239:0.000000 2:@0.422631:0.696581:0.427868:0.696581:0.427868:0.687000:0.422631:0.687000:0.000000 2 1:@0.427821:0.702090:0.467580:0.702090:0.467580:0.688374:0.427821:0.688374:0.000000:0.000000:0.000000 a:@0.443062:0.702645:0.452321:0.702645:0.452321:0.686239:0.443062:0.686239:0.000000 1:@0.467488:0.702645:0.476471:0.702645:0.476471:0.686211:0.467488:0.686211:0.000000 10 8 3:@0.296031:0.716620:0.411950:0.716620:0.411950:0.700186:0.296031:0.700186:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.322958:0.716620:0.332217:0.716620:0.332217:0.700214:0.322958:0.700214:0.000000 4:@0.332151:0.710556:0.337388:0.710556:0.337388:0.700975:0.332151:0.700975:0.000000 2:@0.341298:0.716065:0.356631:0.716065:0.356631:0.702350:0.341298:0.702350:0.000000 a:@0.369388:0.716620:0.378646:0.716620:0.378646:0.700214:0.369388:0.700214:0.000000 3:@0.378578:0.710556:0.383815:0.710556:0.383815:0.700975:0.378578:0.700975:0.000000 2:@0.387726:0.716065:0.403059:0.716065:0.403059:0.702350:0.387726:0.702350:0.000000 a:@0.411877:0.716620:0.421135:0.716620:0.421135:0.700214:0.411877:0.700214:0.000000 2:@0.421055:0.710556:0.426292:0.710556:0.426292:0.700975:0.421055:0.700975:0.000000 6 8:@0.296031:0.730595:0.369700:0.730595:0.369700:0.714162:0.296031:0.714162:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.323179:0.730595:0.332438:0.730595:0.332438:0.714189:0.323179:0.714189:0.000000 4:@0.332372:0.724532:0.337609:0.724532:0.337609:0.714951:0.332372:0.714951:0.000000 2:@0.341519:0.730041:0.356852:0.730041:0.356852:0.716325:0.341519:0.716325:0.000000 a:@0.369608:0.730595:0.378867:0.730595:0.378867:0.714189:0.369608:0.714189:0.000000 3 :@0.378799:0.724532:0.386343:0.724532:0.386343:0.714951:0.378799:0.714951:0.000000:0.000000 2:@0.386292:0.730041:0.401625:0.730041:0.401625:0.716325:0.386292:0.716325:0.000000 6:@0.401533:0.730595:0.410516:0.730595:0.410516:0.714162:0.401533:0.714162:0.000000 a:@0.410442:0.730595:0.419701:0.730595:0.419701:0.714189:0.410442:0.714189:0.000000 2 :@0.419628:0.724532:0.427172:0.724532:0.427172:0.714951:0.419628:0.714951:0.000000:0.000000 2 1:@0.427121:0.730041:0.469192:0.730041:0.469192:0.716325:0.427121:0.716325:0.000000:0.000000:0.000000 a:@0.442362:0.730595:0.451621:0.730595:0.451621:0.714189:0.442362:0.714189:0.000000 :@0.451554:0.724532:0.453904:0.724532:0.453904:0.714951:0.451554:0.714951:0.000000 1:@0.469100:0.730595:0.478082:0.730595:0.478082:0.714162:0.469100:0.714162:0.000000 Simplificamos el polinomio P ::@0.293660:0.754865:0.512380:0.754871:0.512380:0.738437:0.293660:0.738431:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.503988:0.758043:0.509225:0.758043:0.509225:0.748462:0.503988:0.748462:0.000000 2:@0.293665:0.790110:0.302648:0.790110:0.302648:0.773676:0.293665:0.773676:0.000000 a:@0.302574:0.790110:0.311833:0.790110:0.311833:0.773704:0.302574:0.773704:0.000000 5:@0.311754:0.784041:0.316991:0.784041:0.316991:0.774460:0.311754:0.774460:0.000000 :@0.316944:0.790688:0.321545:0.790688:0.321545:0.773033:0.316944:0.773033:0.000000 2:@0.321453:0.789550:0.336787:0.789550:0.336787:0.775835:0.321453:0.775835:0.000000 a:@0.339979:0.790105:0.349238:0.790105:0.349238:0.773699:0.339979:0.773699:0.000000 4:@0.349171:0.784041:0.354408:0.784041:0.354408:0.774460:0.349171:0.774460:0.000000 :@0.354362:0.790105:0.358393:0.790105:0.358393:0.773671:0.354362:0.773671:0.000000 2:@0.358320:0.789550:0.373653:0.789550:0.373653:0.775835:0.358320:0.775835:0.000000 :@0.373561:0.790688:0.378163:0.790688:0.378163:0.773033:0.373561:0.773033:0.000000 7 1:@0.381347:0.790105:0.436772:0.790105:0.436772:0.773671:0.381347:0.773671:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.390250:0.790105:0.399509:0.790105:0.399509:0.773699:0.390250:0.773699:0.000000 2:@0.399443:0.784041:0.404680:0.784041:0.404680:0.774460:0.399443:0.774460:0.000000 1:@0.408590:0.789550:0.423923:0.789550:0.423923:0.775835:0.408590:0.775835:0.000000 :@0.439961:0.790688:0.444563:0.790688:0.444563:0.773033:0.439961:0.773033:0.000000 2:@0.444471:0.789550:0.459804:0.789550:0.459804:0.775835:0.444471:0.775835:0.000000 3:@0.459712:0.790105:0.468695:0.790105:0.468695:0.773671:0.459712:0.773671:0.000000 a:@0.468621:0.790105:0.477880:0.790105:0.477880:0.773699:0.468621:0.773699:0.000000 3:@0.477808:0.784041:0.483045:0.784041:0.483045:0.774460:0.477808:0.774460:0.000000 2:@0.293660:0.825338:0.302643:0.825338:0.302643:0.808904:0.293660:0.808904:0.000000 a:@0.302569:0.825338:0.311828:0.825338:0.311828:0.808932:0.302569:0.808932:0.000000 5:@0.311754:0.819274:0.316991:0.819274:0.316991:0.809693:0.311754:0.809693:0.000000 :@0.316944:0.825920:0.321545:0.825920:0.321545:0.808266:0.316944:0.808266:0.000000 2:@0.321453:0.824783:0.336787:0.824783:0.336787:0.811068:0.321453:0.811068:0.000000 a:@0.339979:0.825338:0.349238:0.825338:0.349238:0.808932:0.339979:0.808932:0.000000 4:@0.349171:0.819274:0.354408:0.819274:0.354408:0.809693:0.349171:0.809693:0.000000 7 1:@0.354362:0.825338:0.428977:0.825338:0.428977:0.808904:0.354362:0.808904:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.358320:0.824783:0.373653:0.824783:0.373653:0.811068:0.358320:0.811068:0.000000 a:@0.382470:0.825338:0.391729:0.825338:0.391729:0.808932:0.382470:0.808932:0.000000 2:@0.391649:0.819274:0.396885:0.819274:0.396885:0.809693:0.391649:0.809693:0.000000 2 2:@0.400795:0.824783:0.448728:0.824783:0.448728:0.811068:0.400795:0.811068:0.000000:0.000000:0.000000 :@0.428885:0.825920:0.433487:0.825920:0.433487:0.808266:0.428885:0.808266:0.000000 3:@0.448636:0.825338:0.457619:0.825338:0.457619:0.808904:0.448636:0.808904:0.000000 a:@0.457545:0.825338:0.466804:0.825338:0.466804:0.808932:0.457545:0.808932:0.000000 3:@0.466728:0.819274:0.471965:0.819274:0.471965:0.809693:0.466728:0.809693:0.000000 2:@0.293660:0.857347:0.302643:0.857347:0.302643:0.840913:0.293660:0.840913:0.000000 a:@0.302569:0.857347:0.311828:0.857347:0.311828:0.840941:0.302569:0.840941:0.000000 5:@0.311754:0.851283:0.316991:0.851283:0.316991:0.841702:0.311754:0.841702:0.000000 :@0.316944:0.857929:0.341296:0.857929:0.341296:0.840275:0.316944:0.840275:0.000000:0.000000:0.000000 2:@0.321453:0.856792:0.336787:0.856792:0.336787:0.843077:0.321453:0.843077:0.000000 a:@0.341204:0.857347:0.350463:0.857347:0.350463:0.840941:0.341204:0.840941:0.000000 4:@0.350398:0.851283:0.355635:0.851283:0.355635:0.841702:0.350398:0.841702:0.000000 :@0.355587:0.857347:0.359618:0.857347:0.359618:0.840913:0.355587:0.840913:0.000000 1:@0.359545:0.856792:0.374878:0.856792:0.374878:0.843077:0.359545:0.843077:0.000000 :@0.374786:0.857929:0.379388:0.857929:0.379388:0.840275:0.374786:0.840275:0.000000 7 1:@0.379296:0.857347:0.434712:0.857347:0.434712:0.840913:0.379296:0.840913:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.388205:0.857347:0.397464:0.857347:0.397464:0.840941:0.388205:0.840941:0.000000 2:@0.397383:0.851283:0.402620:0.851283:0.402620:0.841702:0.397383:0.841702:0.000000 1 1:@0.406530:0.856792:0.454463:0.856792:0.454463:0.843077:0.406530:0.843077:0.000000:0.000000:0.000000 :@0.434620:0.857929:0.439221:0.857929:0.439221:0.840275:0.434620:0.840275:0.000000 3:@0.454371:0.857347:0.463353:0.857347:0.463353:0.840913:0.454371:0.840913:0.000000 a:@0.463280:0.857347:0.472538:0.857347:0.472538:0.840941:0.463280:0.840941:0.000000 3:@0.472463:0.851283:0.477700:0.851283:0.477700:0.841702:0.472463:0.841702:0.000000 2:@0.293660:0.889356:0.302643:0.889356:0.302643:0.872922:0.293660:0.872922:0.000000 a:@0.302569:0.889356:0.311828:0.889356:0.311828:0.872950:0.302569:0.872950:0.000000 5:@0.311754:0.883292:0.316991:0.883292:0.316991:0.873711:0.311754:0.873711:0.000000 :@0.316944:0.889938:0.341296:0.889938:0.341296:0.872284:0.316944:0.872284:0.000000:0.000000:0.000000 2:@0.321453:0.888801:0.336787:0.888801:0.336787:0.875086:0.321453:0.875086:0.000000 a:@0.341204:0.889356:0.350463:0.889356:0.350463:0.872950:0.341204:0.872950:0.000000 4:@0.350398:0.883292:0.355635:0.883292:0.355635:0.873711:0.350398:0.873711:0.000000 :@0.355587:0.889356:0.359618:0.889356:0.359618:0.872922:0.355587:0.872922:0.000000 1:@0.359545:0.888801:0.374878:0.888801:0.374878:0.875086:0.359545:0.875086:0.000000 :@0.374786:0.889938:0.379388:0.889938:0.379388:0.872284:0.374786:0.872284:0.000000 3 7:@0.379296:0.889356:0.434713:0.889356:0.434713:0.872922:0.379296:0.872922:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.388205:0.889356:0.397464:0.889356:0.397464:0.872950:0.388205:0.872950:0.000000 3:@0.397383:0.883292:0.402620:0.883292:0.402620:0.873711:0.397383:0.873711:0.000000 1:@0.406532:0.888801:0.421865:0.888801:0.421865:0.875086:0.406532:0.875086:0.000000 a:@0.434621:0.889356:0.443880:0.889356:0.443880:0.872950:0.434621:0.872950:0.000000 2 :@0.443810:0.883292:0.451354:0.883292:0.451354:0.873711:0.443810:0.873711:0.000000:0.000000 1:@0.451303:0.888801:0.466636:0.888801:0.466636:0.875086:0.451303:0.875086:0.000000 1:@0.466544:0.889356:0.479485:0.889356:0.479485:0.872922:0.466544:0.872922:0.000000:0.000000 Podemos encontrar las :@0.078581:0.449147:0.230267:0.449147:0.230267:0.434207:0.078581:0.434207:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 raíces de polinomios en :@0.078581:0.464276:0.235645:0.464276:0.235645:0.449336:0.078581:0.449336:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 las teclas de un piano. Al :@0.078581:0.479405:0.239348:0.479405:0.239348:0.464465:0.078581:0.464465:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 pulsar una tecla, se activa :@0.078581:0.494534:0.244837:0.494534:0.244837:0.479594:0.078581:0.479594:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 un martillo que golpea :@0.078581:0.509662:0.230083:0.509662:0.230083:0.494723:0.078581:0.494723:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 una cuerda que vibra a :@0.078581:0.524791:0.229850:0.524791:0.229850:0.509852:0.078581:0.509852:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 determinada frecuencia :@0.078581:0.539920:0.236144:0.539920:0.236144:0.524981:0.078581:0.524981:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (velocidad). Esta define la :@0.078581:0.555049:0.243840:0.555049:0.243840:0.540109:0.078581:0.540109:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 nota. La frecuencia es un :@0.078581:0.570178:0.241380:0.570178:0.241380:0.555238:0.078581:0.555238:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 número, y, de hecho, es la :@0.078581:0.585307:0.248087:0.585307:0.248087:0.570367:0.078581:0.570367:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 raíz de un polinomio que :@0.078581:0.600436:0.244598:0.600436:0.244598:0.585496:0.078581:0.585496:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 se define a partir de las :@0.078581:0.615565:0.229497:0.615565:0.229497:0.600625:0.078581:0.600625:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 características de la cuerda. :@0.078581:0.630694:0.257039:0.630694:0.257039:0.615754:0.078581:0.615754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Esto mismo sucede con :@0.078581:0.645823:0.235873:0.645823:0.235873:0.630883:0.078581:0.630883:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cualquier instrumento u :@0.078581:0.660952:0.237762:0.660952:0.237762:0.646012:0.078581:0.646012:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 objeto que vibra.:@0.078581:0.676081:0.187779:0.676081:0.187779:0.661141:0.078581:0.661141:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Responde:@0.078581:0.691210:0.146835:0.691210:0.146835:0.676056:0.078581:0.676056:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 : ¿qué nombre :@0.146571:0.691210:0.243789:0.691210:0.243789:0.676270:0.146571:0.676270:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 recibe el polinomio que :@0.078581:0.706339:0.236157:0.706339:0.236157:0.691399:0.078581:0.691399:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tiene dos monomios?:@0.078581:0.721468:0.219012:0.721468:0.219012:0.706528:0.078581:0.706528:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Interdisciplinariedad :@0.078581:0.384536:0.244955:0.384536:0.244955:0.367589:0.078581:0.367589:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Matemática :@0.078581:0.401178:0.172624:0.401178:0.172624:0.384744:0.078581:0.384744:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y música:@0.078581:0.417820:0.142325:0.417820:0.142325:0.401386:0.078581:0.401386:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Luego, escribimos en forma vertical los polinomios, :@0.573524:0.671115:0.930651:0.671115:0.930651:0.654681:0.573524:0.654681:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cambiando de signo al polinomio sustraendo.:@0.573524:0.687757:0.898491:0.687757:0.898491:0.671323:0.573524:0.671323:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 6 8:@0.696488:0.710580:0.757023:0.710580:0.757023:0.694146:0.696488:0.694146:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.705335:0.710580:0.714594:0.710580:0.714594:0.694174:0.705335:0.694174:0.000000 4:@0.714527:0.704516:0.719764:0.704516:0.719764:0.694935:0.714527:0.694935:0.000000 2:@0.723675:0.710025:0.739009:0.710025:0.739009:0.696309:0.723675:0.696309:0.000000 a:@0.756934:0.710580:0.766193:0.710580:0.766193:0.694174:0.756934:0.694174:0.000000 3 :@0.766127:0.704516:0.773672:0.704516:0.773672:0.694935:0.766127:0.694935:0.000000:0.000000 2:@0.773619:0.710025:0.788952:0.710025:0.788952:0.696309:0.773619:0.696309:0.000000 6:@0.788860:0.710580:0.806973:0.710580:0.806973:0.694146:0.788860:0.694146:0.000000:0.000000:0.000000 a:@0.806886:0.710580:0.816145:0.710580:0.816145:0.694174:0.806886:0.694174:0.000000 2 :@0.816078:0.704516:0.823622:0.704516:0.823622:0.694935:0.816078:0.694935:0.000000:0.000000 2 1:@0.823571:0.710025:0.868893:0.710025:0.868893:0.696309:0.823571:0.696309:0.000000:0.000000:0.000000 :@0.838813:0.704516:0.841163:0.704516:0.841163:0.694935:0.838813:0.694935:0.000000 a :@0.841117:0.710580:0.872115:0.710580:0.872115:0.694174:0.841117:0.694174:0.000000:0.000000:0.000000:0.000000 1:@0.872041:0.710580:0.881024:0.710580:0.881024:0.694146:0.872041:0.694146:0.000000 2:@0.623451:0.724004:0.638784:0.724004:0.638784:0.710289:0.623451:0.710289:0.000000 2 4 3:@0.638692:0.724559:0.754829:0.724555:0.754829:0.708121:0.638692:0.708125:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.647601:0.724559:0.656860:0.724559:0.656860:0.708153:0.647601:0.708153:0.000000 5:@0.656785:0.718491:0.662022:0.718491:0.662022:0.708910:0.656785:0.708910:0.000000 1:@0.665932:0.724000:0.681265:0.724000:0.681265:0.710285:0.665932:0.710285:0.000000 a:@0.703143:0.724555:0.712402:0.724555:0.712402:0.708149:0.703143:0.708149:0.000000 4:@0.712335:0.718491:0.717572:0.718491:0.717572:0.708910:0.712335:0.708910:0.000000 2:@0.721482:0.724000:0.736815:0.724000:0.736815:0.710285:0.721482:0.710285:0.000000 a:@0.754742:0.724555:0.764001:0.724555:0.764001:0.708149:0.754742:0.708149:0.000000 3 :@0.763934:0.718491:0.771478:0.718491:0.771478:0.708910:0.763934:0.708910:0.000000:0.000000 2:@0.771427:0.724000:0.786760:0.724000:0.786760:0.710285:0.771427:0.710285:0.000000 7 :@0.786668:0.724555:0.841442:0.724555:0.841442:0.708121:0.786668:0.708121:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.804694:0.724555:0.813953:0.724555:0.813953:0.708149:0.804694:0.708149:0.000000 2:@0.813886:0.718491:0.819123:0.718491:0.819123:0.708910:0.813886:0.708910:0.000000 2:@0.855729:0.724000:0.871062:0.724000:0.871062:0.710285:0.855729:0.710285:0.000000 1:@0.870970:0.724555:0.879953:0.724555:0.879953:0.708121:0.870970:0.708121:0.000000 2:@0.623448:0.737980:0.638781:0.737980:0.638781:0.724264:0.623448:0.724264:0.000000 2 10 11:@0.638689:0.738534:0.754394:0.738529:0.754394:0.722095:0.638689:0.722101:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.647598:0.738534:0.656857:0.738534:0.656857:0.722128:0.647598:0.722128:0.000000 5:@0.656785:0.732465:0.662022:0.732465:0.662022:0.722884:0.656785:0.722884:0.000000 1:@0.665932:0.737975:0.681265:0.737975:0.681265:0.724259:0.665932:0.724259:0.000000 a:@0.702930:0.738529:0.712189:0.738529:0.712189:0.722123:0.702930:0.722123:0.000000 4:@0.712114:0.732465:0.717351:0.732465:0.717351:0.722884:0.712114:0.722884:0.000000 2:@0.721261:0.737975:0.736594:0.737975:0.736594:0.724259:0.721261:0.724259:0.000000 a:@0.754302:0.738529:0.763560:0.738529:0.763560:0.722123:0.754302:0.722123:0.000000 3 :@0.763492:0.732465:0.771036:0.732465:0.771036:0.722884:0.763492:0.722884:0.000000:0.000000 2:@0.770985:0.737975:0.786319:0.737975:0.786319:0.724259:0.770985:0.724259:0.000000 13:@0.786227:0.738529:0.804118:0.738529:0.804118:0.722095:0.786227:0.722095:0.000000:0.000000 a:@0.804026:0.738529:0.813285:0.738529:0.813285:0.722123:0.804026:0.722123:0.000000 2 :@0.813223:0.732465:0.820767:0.732465:0.820767:0.722884:0.813223:0.722884:0.000000:0.000000 2 :@0.820717:0.737975:0.840560:0.737975:0.840560:0.724259:0.820717:0.724259:0.000000:0.000000 a:@0.840468:0.738529:0.849727:0.738529:0.849727:0.722123:0.840468:0.722123:0.000000 El polinomio resultante de la operación es: :@0.573526:0.761911:0.884827:0.761911:0.884827:0.745477:0.573526:0.745477:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.632300:0.793364:0.647633:0.793364:0.647633:0.779648:0.632300:0.779648:0.000000 2:@0.647541:0.793919:0.656524:0.793919:0.656524:0.777485:0.647541:0.777485:0.000000 a:@0.656450:0.793919:0.665709:0.793919:0.665709:0.777513:0.656450:0.777513:0.000000 5:@0.665626:0.787857:0.670862:0.787857:0.670862:0.778277:0.665626:0.778277:0.000000 :@0.670815:0.794504:0.695168:0.794504:0.695168:0.776850:0.670815:0.776850:0.000000:0.000000:0.000000 1:@0.675324:0.793367:0.690658:0.793367:0.690658:0.779651:0.675324:0.779651:0.000000 10 :@0.695075:0.793921:0.731294:0.793921:0.731294:0.777488:0.695075:0.777488:0.000000:0.000000:0.000000:0.000000 a:@0.712875:0.793921:0.722134:0.793921:0.722134:0.777515:0.712875:0.777515:0.000000 4:@0.722072:0.787857:0.727309:0.787857:0.727309:0.778277:0.722072:0.778277:0.000000 2:@0.731221:0.793367:0.746554:0.793367:0.746554:0.779651:0.731221:0.779651:0.000000 :@0.746462:0.794504:0.751064:0.794504:0.751064:0.776850:0.746462:0.776850:0.000000 11 :@0.750972:0.793921:0.787182:0.793921:0.787182:0.777488:0.750972:0.777488:0.000000:0.000000:0.000000:0.000000 a:@0.768771:0.793921:0.778030:0.793921:0.778030:0.777515:0.768771:0.777515:0.000000 3:@0.777962:0.787857:0.783199:0.787857:0.783199:0.778277:0.777962:0.778277:0.000000 2 :@0.787108:0.793367:0.806951:0.793367:0.806951:0.779651:0.787108:0.779651:0.000000:0.000000 13:@0.806859:0.793921:0.824751:0.793921:0.824751:0.777488:0.806859:0.777488:0.000000:0.000000 a:@0.824659:0.793921:0.833918:0.793921:0.833918:0.777515:0.824659:0.777515:0.000000 2 :@0.833849:0.787857:0.841394:0.787857:0.841394:0.778277:0.833849:0.778277:0.000000:0.000000 2:@0.841343:0.793367:0.856676:0.793367:0.856676:0.779651:0.841343:0.779651:0.000000 :@0.856584:0.787857:0.858934:0.787857:0.858934:0.778277:0.856584:0.778277:0.000000 a:@0.858887:0.793921:0.868145:0.793921:0.868145:0.777515:0.858887:0.777515:0.000000 MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000