134:@0.026565:0.967627:0.050760:0.967627:0.050760:0.951847:0.026565:0.951847:0.000000:0.000000:0.000000
1.:@0.404236:0.105212:0.416508:0.105212:0.416508:0.088498:0.404236:0.088498:0.000000:0.000000
  En la figura 3.14. se muestran las gráficas de las parábolas   y  .:@0.416508:0.104995:0.877842:0.104995:0.877842:0.088498:0.416508:0.088498:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P:@0.832362:0.105111:0.841147:0.105111:0.841147:0.088642:0.832362:0.088642:0.000000
1:@0.841152:0.107668:0.845675:0.107668:0.845675:0.098886:0.841152:0.098886:0.000000
P:@0.861781:0.105111:0.870566:0.105111:0.870566:0.088642:0.861781:0.088642:0.000000
2:@0.870566:0.107668:0.875088:0.107668:0.875088:0.098886:0.870566:0.098886:0.000000
 :@0.404245:0.129474:0.408387:0.129474:0.408387:0.112977:0.404245:0.112977:0.000000
  Nótese que se ha supuesto que  > 0,   > 0. Se observa que :@0.427698:0.129474:0.895952:0.129474:0.895952:0.112977:0.427698:0.112977:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a :@0.671471:0.129590:0.684591:0.129590:0.684591:0.113121:0.671471:0.113121:0.000000:0.000000
α:@0.723489:0.130024:0.735645:0.130024:0.735645:0.111184:0.723489:0.111184:0.000000
estas dos gráficas se cortan en dos puntos distintos, de abs-:@0.427690:0.146825:0.891771:0.146825:0.891771:0.130327:0.427690:0.130327:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cisas   y  . Es  decir que :@0.427690:0.167313:0.630778:0.167320:0.630778:0.150822:0.427690:0.150816:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.469053:0.167429:0.476528:0.167429:0.476528:0.150960:0.469053:0.150960:0.000000
1:@0.476518:0.169991:0.481040:0.169991:0.481040:0.161209:0.476518:0.161209:0.000000
x:@0.507126:0.167435:0.514601:0.167435:0.514601:0.150967:0.507126:0.150967:0.000000
2:@0.514584:0.169991:0.519107:0.169991:0.519107:0.161209:0.514584:0.161209:0.000000
xy:@0.646163:0.166178:0.674059:0.166178:0.674059:0.149709:0.646163:0.149709:0.000000:0.000000
xy:@0.703168:0.166178:0.732683:0.166178:0.732683:0.149709:0.703168:0.149709:0.000000:0.000000
P:@0.763168:0.166178:0.771953:0.166178:0.771953:0.149709:0.763168:0.149709:0.000000
P:@0.794108:0.166178:0.802893:0.166178:0.802893:0.149709:0.794108:0.149709:0.000000
(:@0.637890:0.169576:0.644306:0.169576:0.644306:0.146457:0.637890:0.146457:0.000000
) (:@0.680871:0.169576:0.701311:0.169576:0.701311:0.146457:0.680871:0.146457:0.000000:0.000000:0.000000
):@0.741133:0.169576:0.747548:0.169576:0.747548:0.146457:0.741133:0.146457:0.000000
∈∩:@0.749922:0.166699:0.791997:0.166699:0.791997:0.150418:0.749922:0.150418:0.000000:0.000000
,:@0.661032:0.166062:0.663787:0.166062:0.663787:0.149565:0.661032:0.149565:0.000000
,:@0.688986:0.166062:0.691741:0.166062:0.691741:0.149565:0.688986:0.149565:0.000000
,:@0.719664:0.166062:0.722419:0.166062:0.722419:0.149565:0.719664:0.149565:0.000000
,  más aún, :@0.808766:0.166062:0.895928:0.167320:0.895928:0.150822:0.808766:0.149565:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.653859:0.168281:0.658776:0.168281:0.658776:0.158732:0.653859:0.158732:0.000000
1:@0.674064:0.168281:0.678981:0.168281:0.678981:0.158732:0.674064:0.158732:0.000000
2:@0.711341:0.168281:0.716258:0.168281:0.716258:0.158732:0.711341:0.158732:0.000000
2:@0.733174:0.168281:0.738091:0.168281:0.738091:0.158732:0.733174:0.158732:0.000000
1:@0.769031:0.168281:0.773949:0.168281:0.773949:0.158732:0.769031:0.158732:0.000000
2:@0.800443:0.168281:0.805360:0.168281:0.805360:0.158732:0.800443:0.158732:0.000000
P:@0.430254:0.186672:0.439039:0.186672:0.439039:0.170203:0.430254:0.170203:0.000000
P:@0.461194:0.186672:0.469979:0.186672:0.469979:0.170203:0.461194:0.170203:0.000000
xy:@0.507373:0.186672:0.535269:0.186672:0.535269:0.170203:0.507373:0.170203:0.000000:0.000000
xy:@0.561817:0.186672:0.591331:0.186672:0.591331:0.170203:0.561817:0.170203:0.000000:0.000000
{:@0.490405:0.191680:0.499653:0.191680:0.499653:0.165305:0.490405:0.165305:0.000000
}:@0.605631:0.191680:0.614878:0.191680:0.614878:0.165305:0.605631:0.165305:0.000000
(:@0.499097:0.190070:0.505512:0.190070:0.505512:0.166951:0.499097:0.166951:0.000000
) (:@0.542077:0.190070:0.559957:0.190070:0.559957:0.166951:0.542077:0.166951:0.000000:0.000000:0.000000
):@0.599779:0.190070:0.606194:0.190070:0.606194:0.166951:0.599779:0.166951:0.000000
∩:@0.444284:0.187193:0.459080:0.187193:0.459080:0.170912:0.444284:0.170912:0.000000
=:@0.477575:0.186556:0.488383:0.186556:0.488383:0.170059:0.477575:0.170059:0.000000
,:@0.522232:0.186556:0.524987:0.186556:0.524987:0.170059:0.522232:0.170059:0.000000
,:@0.550186:0.186556:0.552941:0.186556:0.552941:0.170059:0.550186:0.170059:0.000000
,:@0.578294:0.186556:0.581049:0.186556:0.581049:0.170059:0.578294:0.170059:0.000000
.:@0.615842:0.186556:0.618597:0.186556:0.618597:0.170059:0.615842:0.170059:0.000000
1:@0.436118:0.188775:0.441035:0.188775:0.441035:0.179226:0.436118:0.179226:0.000000
2:@0.467529:0.188775:0.472447:0.188775:0.472447:0.179226:0.467529:0.179226:0.000000
1:@0.515065:0.188775:0.519982:0.188775:0.519982:0.179226:0.515065:0.179226:0.000000
1:@0.535270:0.188775:0.540187:0.188775:0.540187:0.179226:0.535270:0.179226:0.000000
2:@0.569982:0.188775:0.574900:0.188775:0.574900:0.179226:0.569982:0.179226:0.000000
2:@0.591815:0.188775:0.596733:0.188775:0.596733:0.179226:0.591815:0.179226:0.000000
 :@0.404236:0.211035:0.408378:0.211035:0.408378:0.194537:0.404236:0.194537:0.000000
  Este par de puntos son solución del par de ecuaciones :@0.427690:0.211035:0.895924:0.211035:0.895924:0.194537:0.427690:0.194537:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.458677:0.255060:0.470834:0.255060:0.475606:0.238780:0.463450:0.238780:0.000000
β:@0.505530:0.255060:0.516107:0.255060:0.520879:0.238780:0.510303:0.238780:0.000000
λ:@0.542866:0.255060:0.553443:0.255060:0.558216:0.238780:0.547639:0.238780:0.000000
+:@0.488372:0.231289:0.498948:0.231289:0.498948:0.215008:0.488372:0.215008:0.000000
+:@0.521778:0.231289:0.532354:0.231289:0.532354:0.215008:0.521778:0.215008:0.000000
+:@0.493083:0.255060:0.503659:0.255060:0.503659:0.238780:0.493083:0.238780:0.000000
+:@0.530419:0.255060:0.540995:0.255060:0.540995:0.238780:0.530419:0.238780:0.000000
=:@0.447482:0.230654:0.458289:0.230654:0.458289:0.214156:0.447482:0.214156:0.000000
,:@0.544174:0.230654:0.546929:0.230654:0.546929:0.214156:0.544174:0.214156:0.000000
=:@0.447482:0.254424:0.458289:0.254424:0.458289:0.237927:0.447482:0.237927:0.000000
.:@0.556484:0.254424:0.559239:0.254424:0.559239:0.237927:0.556484:0.237927:0.000000
2:@0.478634:0.222617:0.483551:0.222617:0.483551:0.213068:0.478634:0.213068:0.000000
2:@0.483350:0.246384:0.488268:0.246384:0.488268:0.236836:0.483350:0.236836:0.000000
yax:@0.436282:0.230768:0.477419:0.230768:0.477419:0.214299:0.436282:0.214299:0.000000:0.000000:0.000000
bxc:@0.501674:0.230768:0.542670:0.230768:0.542670:0.214299:0.501674:0.214299:0.000000:0.000000:0.000000
y:@0.436282:0.254540:0.443969:0.254540:0.443969:0.238071:0.436282:0.238071:0.000000
x:@0.474658:0.254540:0.482133:0.254540:0.482133:0.238071:0.474658:0.238071:0.000000
x:@0.519519:0.254540:0.526994:0.254540:0.526994:0.238071:0.519519:0.238071:0.000000
 :@0.404236:0.286211:0.408378:0.286211:0.408378:0.269713:0.404236:0.269713:0.000000
  Procediendo en forma similar al caso de intersección de una recta :@0.427689:0.286211:0.895823:0.286211:0.895823:0.269713:0.427689:0.269713:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
con una parábola, al igualar miembro a miembro, se tiene::@0.427681:0.303562:0.837796:0.303562:0.837796:0.287064:0.427681:0.287064:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404236:0.338726:0.408378:0.338726:0.408378:0.322228:0.404236:0.322228:0.000000
x:@0.440170:0.330193:0.447701:0.330193:0.447701:0.313601:0.440170:0.313601:0.000000
2:@0.448925:0.321980:0.453879:0.321980:0.453879:0.312359:0.448925:0.312359:0.000000
+:@0.457363:0.330717:0.468019:0.330717:0.468019:0.314314:0.457363:0.314314:0.000000
x:@0.482892:0.330193:0.490423:0.330193:0.490423:0.313601:0.482892:0.313601:0.000000
+:@0.492810:0.330717:0.503466:0.330717:0.503466:0.314314:0.492810:0.314314:0.000000
=:@0.520444:0.330076:0.531333:0.330076:0.531333:0.313455:0.520444:0.313455:0.000000
ax:@0.534108:0.330193:0.550510:0.330193:0.550510:0.313601:0.534108:0.313601:0.000000:0.000000
2:@0.551723:0.321980:0.556677:0.321980:0.556677:0.312359:0.551723:0.312359:0.000000
+:@0.560161:0.330717:0.570817:0.330717:0.570817:0.314314:0.560161:0.314314:0.000000
bx c:@0.572563:0.330193:0.611809:0.330193:0.611809:0.313601:0.572563:0.313601:0.000000:0.000000:0.000000:0.000000
+:@0.591759:0.330717:0.602415:0.330717:0.602415:0.314314:0.591759:0.314314:0.000000
a:@0.644234:0.330193:0.653279:0.330193:0.653279:0.313601:0.644234:0.313601:0.000000
(:@0.637061:0.333773:0.643524:0.333773:0.643524:0.312121:0.637061:0.312121:0.000000
):@0.680635:0.333773:0.687099:0.333773:0.687099:0.312121:0.680635:0.312121:0.000000
x:@0.689171:0.330193:0.696702:0.330193:0.696702:0.313601:0.689171:0.313601:0.000000
2:@0.697926:0.321980:0.702880:0.321980:0.702880:0.312359:0.697926:0.312359:0.000000
+:@0.706366:0.330717:0.717022:0.330717:0.717022:0.314314:0.706366:0.314314:0.000000
b:@0.725503:0.330193:0.734839:0.330193:0.734839:0.313601:0.725503:0.313601:0.000000
(:@0.718761:0.333773:0.725224:0.333773:0.725224:0.312121:0.718761:0.312121:0.000000
):@0.762335:0.333773:0.768798:0.333773:0.768798:0.312121:0.762335:0.312121:0.000000
x c:@0.770871:0.330193:0.800839:0.330193:0.800839:0.313601:0.770871:0.313601:0.000000:0.000000:0.000000
+:@0.780789:0.330717:0.791445:0.330717:0.791445:0.314314:0.780789:0.314314:0.000000
=0.:@0.830787:0.330076:0.855709:0.330076:0.855709:0.313455:0.830787:0.313455:0.000000:0.000000:0.000000
 :@0.859901:0.338728:0.864043:0.338728:0.864043:0.322230:0.859901:0.322230:0.000000
 :@0.404240:0.363207:0.408382:0.363207:0.408382:0.346709:0.404240:0.346709:0.000000
  Si  ≠  ,  – :@0.427693:0.363207:0.527595:0.363207:0.527595:0.346709:0.427693:0.346709:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a :@0.445467:0.363322:0.458587:0.363322:0.458587:0.346854:0.445467:0.346854:0.000000:0.000000
α:@0.477159:0.363756:0.489315:0.363756:0.489315:0.344916:0.477159:0.344916:0.000000
a :@0.498023:0.363322:0.511142:0.363322:0.511142:0.346854:0.498023:0.346854:0.000000:0.000000
α :@0.529406:0.363756:0.546379:0.363756:0.546379:0.344916:0.529406:0.344916:0.000000:0.000000
≠ 0, y podemos dividir la última ecuación para  :@0.548498:0.363207:0.895908:0.363207:0.895908:0.346709:0.548498:0.346709:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a :@0.427685:0.380673:0.440805:0.380673:0.440805:0.364204:0.427685:0.364204:0.000000:0.000000
–  , resulta::@0.440805:0.380557:0.524667:0.380557:0.524667:0.364060:0.440805:0.364060:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.455447:0.381107:0.467603:0.381107:0.467603:0.362267:0.455447:0.362267:0.000000
x:@0.405141:0.418791:0.412616:0.418791:0.412616:0.402322:0.405141:0.402322:0.000000
2:@0.413832:0.410640:0.418749:0.410640:0.418749:0.401091:0.413832:0.401091:0.000000
+:@0.422206:0.419312:0.432783:0.419312:0.432783:0.403031:0.422206:0.403031:0.000000
b:@0.436020:0.409957:0.445286:0.409957:0.445286:0.393488:0.436020:0.393488:0.000000
a:@0.436446:0.430146:0.445424:0.430146:0.445424:0.413677:0.436446:0.413677:0.000000
x:@0.475868:0.418791:0.483343:0.418791:0.483343:0.402322:0.475868:0.402322:0.000000
+:@0.485712:0.419312:0.496289:0.419312:0.496289:0.403031:0.485712:0.403031:0.000000
c:@0.500797:0.409957:0.507983:0.409957:0.507983:0.393488:0.500797:0.393488:0.000000
a:@0.499949:0.430146:0.508927:0.430146:0.508927:0.413677:0.499949:0.413677:0.000000
=0:@0.539998:0.418676:0.562056:0.418676:0.562056:0.402178:0.539998:0.402178:0.000000:0.000000
x:@0.599681:0.418791:0.607156:0.418791:0.607156:0.402322:0.599681:0.402322:0.000000
+:@0.609526:0.419312:0.620103:0.419312:0.620103:0.403031:0.609526:0.403031:0.000000
b:@0.634918:0.409957:0.644184:0.409957:0.644184:0.393488:0.634918:0.393488:0.000000
2:@0.623341:0.430030:0.631837:0.430030:0.631837:0.413533:0.623341:0.413533:0.000000
a:@0.640198:0.430146:0.649175:0.430146:0.649175:0.413677:0.640198:0.413677:0.000000
(:@0.633079:0.433701:0.639494:0.433701:0.639494:0.412210:0.633079:0.412210:0.000000
):@0.676329:0.433701:0.682745:0.433701:0.682745:0.412210:0.676329:0.412210:0.000000
2:@0.692078:0.395826:0.696995:0.395826:0.696995:0.386278:0.692078:0.386278:0.000000
b:@0.733749:0.409951:0.743016:0.409951:0.743016:0.393482:0.733749:0.393482:0.000000
2:@0.722180:0.430030:0.730676:0.430030:0.730676:0.413533:0.722180:0.413533:0.000000
a:@0.739037:0.430146:0.748015:0.430146:0.748015:0.413677:0.739037:0.413677:0.000000
(:@0.731918:0.433701:0.738333:0.433701:0.738333:0.412210:0.731918:0.412210:0.000000
):@0.775169:0.433701:0.781584:0.433701:0.781584:0.412210:0.775169:0.412210:0.000000
2:@0.790917:0.395826:0.795834:0.395826:0.795834:0.386278:0.790917:0.386278:0.000000
+:@0.799293:0.419312:0.809870:0.419312:0.809870:0.403031:0.799293:0.403031:0.000000
c:@0.814378:0.409957:0.821564:0.409957:0.821564:0.393488:0.814378:0.393488:0.000000
a:@0.813532:0.430146:0.822510:0.430146:0.822510:0.413677:0.813532:0.413677:0.000000
=0:@0.853582:0.418676:0.875641:0.418676:0.875641:0.402178:0.853582:0.402178:0.000000:0.000000
x:@0.439129:0.479837:0.446604:0.479837:0.446604:0.463368:0.439129:0.463368:0.000000
+:@0.448973:0.480358:0.459550:0.480358:0.459550:0.464077:0.448973:0.464077:0.000000
b:@0.474365:0.471003:0.483632:0.471003:0.483632:0.454534:0.474365:0.454534:0.000000
2:@0.462791:0.491081:0.471287:0.491081:0.471287:0.474583:0.462791:0.474583:0.000000
a:@0.479648:0.491197:0.488626:0.491197:0.488626:0.474728:0.479648:0.474728:0.000000
(:@0.472529:0.494750:0.478944:0.494750:0.478944:0.473260:0.472529:0.473260:0.000000
):@0.515780:0.494750:0.522195:0.494750:0.522195:0.473260:0.515780:0.473260:0.000000
2:@0.531528:0.456877:0.536445:0.456877:0.536445:0.447328:0.531528:0.447328:0.000000
=:@0.541160:0.479726:0.551968:0.479726:0.551968:0.463229:0.541160:0.463229:0.000000
b:@0.574874:0.471008:0.584141:0.471008:0.584141:0.454539:0.574874:0.454539:0.000000
2:@0.563305:0.491081:0.571801:0.491081:0.571801:0.474583:0.563305:0.474583:0.000000
a:@0.580162:0.491197:0.589140:0.491197:0.589140:0.474728:0.580162:0.474728:0.000000
(:@0.573043:0.494750:0.579459:0.494750:0.579459:0.473260:0.573043:0.473260:0.000000
):@0.616294:0.494750:0.622709:0.494750:0.622709:0.473260:0.616294:0.473260:0.000000
2:@0.632042:0.456877:0.636959:0.456877:0.636959:0.447328:0.632042:0.447328:0.000000
c:@0.655914:0.471001:0.663100:0.471001:0.663100:0.454532:0.655914:0.454532:0.000000
a:@0.655077:0.491197:0.664054:0.491197:0.664054:0.474728:0.655077:0.474728:0.000000
.:@0.693765:0.479726:0.696519:0.479726:0.696519:0.463229:0.693765:0.463229:0.000000
  :@0.891769:0.488848:0.895911:0.488848:0.895911:0.472350:0.891769:0.472350:0.000000:0.000000
De esta última igualdad, para que existan dos puntos de corte  :@0.404242:0.555156:0.895911:0.555156:0.895911:0.538659:0.404242:0.538659:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
distintos, se debe verificar que::@0.404242:0.572507:0.620262:0.572507:0.620262:0.556009:0.404242:0.556009:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.442233:0.634073:0.446375:0.634073:0.446375:0.617576:0.442233:0.617576:0.000000
b:@0.486814:0.603782:0.496080:0.603782:0.496080:0.587313:0.486814:0.587313:0.000000
2:@0.475245:0.623862:0.483741:0.623862:0.483741:0.607364:0.475245:0.607364:0.000000
a:@0.492102:0.623978:0.501079:0.623978:0.501079:0.607509:0.492102:0.607509:0.000000
(:@0.484981:0.627531:0.491396:0.627531:0.491396:0.606041:0.484981:0.606041:0.000000
):@0.528232:0.627531:0.534647:0.627531:0.534647:0.606041:0.528232:0.606041:0.000000
2:@0.543981:0.589658:0.548899:0.589658:0.548899:0.580109:0.543981:0.580109:0.000000
c:@0.567853:0.603782:0.575039:0.603782:0.575039:0.587313:0.567853:0.587313:0.000000
a:@0.567016:0.623978:0.575993:0.623978:0.575993:0.607509:0.567016:0.607509:0.000000
=:@0.607064:0.612506:0.617872:0.612506:0.617872:0.596008:0.607064:0.596008:0.000000
b:@0.628429:0.602399:0.637696:0.602399:0.637696:0.585931:0.628429:0.585931:0.000000
(:@0.621722:0.605961:0.628138:0.605961:0.628138:0.584470:0.621722:0.584470:0.000000
):@0.664973:0.605961:0.671388:0.605961:0.671388:0.584470:0.664973:0.584470:0.000000
2:@0.671666:0.591936:0.676584:0.591936:0.676584:0.582388:0.671666:0.582388:0.000000
4:@0.693183:0.602291:0.701679:0.602291:0.701679:0.585793:0.693183:0.585793:0.000000
a:@0.710040:0.602406:0.719018:0.602406:0.719018:0.585937:0.710040:0.585937:0.000000
(:@0.702920:0.605961:0.709335:0.605961:0.709335:0.584470:0.702920:0.584470:0.000000
)(:@0.746170:0.605961:0.759907:0.605961:0.759907:0.584470:0.746170:0.584470:0.000000:0.000000
c:@0.760612:0.602406:0.767798:0.602406:0.767798:0.585937:0.760612:0.585937:0.000000
):@0.795105:0.605961:0.801520:0.605961:0.801520:0.584470:0.795105:0.584470:0.000000
4:@0.678525:0.625748:0.687021:0.625748:0.687021:0.609250:0.678525:0.609250:0.000000
a:@0.695382:0.625864:0.704360:0.625864:0.704360:0.609395:0.695382:0.609395:0.000000
(:@0.688261:0.629417:0.694677:0.629417:0.694677:0.607927:0.688261:0.607927:0.000000
):@0.731512:0.629417:0.737927:0.629417:0.737927:0.607927:0.731512:0.607927:0.000000
2:@0.738205:0.615394:0.743123:0.615394:0.743123:0.605845:0.738205:0.605845:0.000000
>0.:@0.804954:0.612506:0.828862:0.612506:0.828862:0.596008:0.804954:0.596008:0.000000:0.000000:0.000000
  En el caso  = :@0.442223:0.658554:0.566694:0.658554:0.566694:0.642056:0.442223:0.642056:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a :@0.538625:0.658669:0.551744:0.658669:0.551744:0.642201:0.538625:0.642201:0.000000:0.000000
α,    α:@0.566694:0.659103:0.629075:0.659103:0.629075:0.640263:0.566694:0.640263:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.588483:0.658669:0.597461:0.658669:0.597461:0.642201:0.588483:0.642201:0.000000
–   = 0, resulta: ( –  )   +   –   = 0.:@0.602277:0.658554:0.865999:0.658554:0.865999:0.642056:0.602277:0.642056:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b :@0.723822:0.658669:0.737230:0.658669:0.737230:0.642201:0.723822:0.642201:0.000000:0.000000
β:@0.751872:0.659103:0.762448:0.659103:0.762448:0.640263:0.751872:0.640263:0.000000
x c:@0.772543:0.658669:0.806296:0.658669:0.806296:0.642201:0.772543:0.642201:0.000000:0.000000:0.000000
λ:@0.825080:0.659103:0.835656:0.659103:0.835656:0.640263:0.825080:0.640263:0.000000
   Si  –   = 0, se tiene  =   con lo que   =   contradice el :@0.442223:0.683033:0.895939:0.683033:0.895939:0.666535:0.442223:0.666535:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b :@0.481582:0.683148:0.494991:0.683148:0.494991:0.666679:0.481582:0.666679:0.000000:0.000000
β:@0.511790:0.683582:0.522367:0.683582:0.522367:0.664742:0.511790:0.664742:0.000000
b :@0.620654:0.683148:0.634063:0.683148:0.634063:0.666679:0.620654:0.666679:0.000000:0.000000
β,:@0.651155:0.683582:0.666548:0.683582:0.666548:0.664742:0.651155:0.664742:0.000000:0.000000
c:@0.754841:0.683148:0.762027:0.683148:0.762027:0.666679:0.754841:0.666679:0.000000
λ:@0.783276:0.683582:0.793853:0.683582:0.793853:0.664742:0.783276:0.664742:0.000000
supuesto de que   ≠  . En consecuencia,  –   ≠ 0, en cuyo :@0.464552:0.700383:0.895932:0.700384:0.895932:0.683886:0.464552:0.683886:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P:@0.586208:0.700499:0.594993:0.700499:0.594993:0.684030:0.586208:0.684030:0.000000
1:@0.594982:0.703055:0.599505:0.703055:0.599505:0.694273:0.594982:0.694273:0.000000
P:@0.618328:0.700500:0.627113:0.700500:0.627113:0.684031:0.618328:0.684031:0.000000
2:@0.627108:0.703055:0.631631:0.703055:0.631631:0.694273:0.627108:0.694273:0.000000
b :@0.763308:0.700500:0.776716:0.700500:0.776716:0.684031:0.763308:0.684031:0.000000:0.000000
β:@0.791090:0.700933:0.801667:0.700933:0.801667:0.682093:0.791090:0.682093:0.000000
caso, la solución de la ecuación precedente es  ˆ =:@0.464563:0.729302:0.840438:0.729302:0.840438:0.712804:0.464563:0.712804:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
,  :@0.885904:0.729302:0.895912:0.729301:0.895912:0.712803:0.885904:0.712804:0.000000:0.000000:0.000000
λ:@0.868149:0.720625:0.878726:0.720625:0.883498:0.704344:0.872922:0.704344:0.000000
β:@0.868571:0.740940:0.879148:0.740940:0.883920:0.724659:0.873344:0.724659:0.000000
−:@0.855700:0.720625:0.866277:0.720625:0.866277:0.704344:0.855700:0.704344:0.000000
−:@0.856124:0.740940:0.866700:0.740940:0.866700:0.724659:0.856124:0.724659:0.000000
x:@0.818422:0.729416:0.825897:0.729416:0.825897:0.712947:0.818422:0.712947:0.000000
c:@0.845586:0.720105:0.852772:0.720105:0.852772:0.703636:0.845586:0.703636:0.000000
b:@0.844391:0.740420:0.853658:0.740420:0.853658:0.723951:0.844391:0.723951:0.000000
 :@0.891770:0.729301:0.895912:0.729301:0.895912:0.712803:0.891770:0.712803:0.000000
b :@0.464544:0.758335:0.477952:0.758335:0.477952:0.741866:0.464544:0.741866:0.000000:0.000000
≠ :@0.477952:0.758219:0.492902:0.758219:0.492902:0.741721:0.477952:0.741721:0.000000:0.000000
β, :@0.492902:0.758768:0.513111:0.758768:0.513111:0.739928:0.492902:0.739928:0.000000:0.000000:0.000000
de donde  ˆ = ˆ:@0.513111:0.758219:0.631806:0.755783:0.631806:0.739285:0.513111:0.741721:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ˆ:@0.665038:0.755783:0.672744:0.755783:0.672744:0.739285:0.665038:0.739285:0.000000
2:@0.632633:0.748926:0.637551:0.748926:0.637551:0.739377:0.632633:0.739377:0.000000
+:@0.642370:0.757599:0.619540:0.757599:0.619540:0.741318:0.642370:0.741318:0.000000
+:@0.675776:0.757599:0.652946:0.757599:0.652946:0.741318:0.675776:0.741318:0.000000
yax:@0.590280:0.757078:0.631411:0.757078:0.631411:0.740609:0.590280:0.740609:0.000000:0.000000:0.000000
bxc:@0.655666:0.757078:0.696669:0.757078:0.696669:0.740609:0.655666:0.740609:0.000000:0.000000:0.000000
, luego  ˆ, ˆ:@0.700062:0.758220:0.783323:0.757040:0.783323:0.740543:0.700062:0.741722:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.812685:0.760439:0.817602:0.760439:0.817602:0.750890:0.812685:0.750890:0.000000
2:@0.844096:0.760439:0.849014:0.760439:0.849014:0.750890:0.844096:0.750890:0.000000
( ):@0.752586:0.761155:0.791193:0.761155:0.791193:0.739176:0.752586:0.739176:0.000000:0.000000:0.000000
∈∩:@0.793575:0.758856:0.835651:0.758856:0.835651:0.742575:0.793575:0.742575:0.000000:0.000000
xy:@0.760863:0.758335:0.783365:0.758335:0.783365:0.741867:0.760863:0.741867:0.000000:0.000000
P:@0.806821:0.758335:0.815606:0.758335:0.815606:0.741867:0.806821:0.741867:0.000000
P:@0.837761:0.758335:0.846546:0.758335:0.846546:0.741867:0.837761:0.741867:0.000000
.:@0.852627:0.758220:0.855382:0.758220:0.855382:0.741722:0.852627:0.741722:0.000000
   Se deja como ejercicio trazar las gráficas de las parábolas que :@0.442220:0.782699:0.895924:0.782699:0.895924:0.766201:0.442220:0.766201:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
satisfacen esta condición.:@0.464548:0.800050:0.643424:0.800050:0.643424:0.783552:0.464548:0.783552:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
   En la figura 3.15. se muestran las gráficas de las parábo-:@0.442220:0.824529:0.891784:0.824529:0.891784:0.808031:0.442220:0.808031:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
las   y  . Se observa que estas dos gráficas no se cortan.  :@0.464548:0.841879:0.895922:0.841878:0.895922:0.825380:0.464548:0.825382:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P:@0.488938:0.841995:0.497723:0.841995:0.497723:0.825526:0.488938:0.825526:0.000000
1:@0.497713:0.844550:0.502235:0.844550:0.502235:0.835769:0.497713:0.835769:0.000000
P:@0.522733:0.841994:0.531518:0.841994:0.531518:0.825525:0.522733:0.825525:0.000000
2:@0.531504:0.844550:0.536027:0.844550:0.536027:0.835769:0.531504:0.835769:0.000000
Se ha supuesto que   > 0,   < 0. El análisis matemático res-:@0.464553:0.859229:0.891780:0.859229:0.891780:0.842731:0.464553:0.842731:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.609871:0.859344:0.618849:0.859344:0.618849:0.842876:0.609871:0.842876:0.000000
α:@0.655761:0.859778:0.667917:0.859778:0.667917:0.840938:0.655761:0.840938:0.000000
pectivo se deja como ejercicio.:@0.464553:0.876580:0.681035:0.876580:0.681035:0.860082:0.464553:0.860082:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
λ:@0.316184:0.199730:0.324047:0.199730:0.324047:0.185723:0.316184:0.185723:0.000000
y=  x:@0.214589:0.187991:0.246788:0.187991:0.246788:0.175510:0.214589:0.175510:0.000000:0.000000:0.000000:0.000000:0.000000
α +β +λ:@0.231977:0.188120:0.288382:0.188120:0.288382:0.174113:0.231977:0.174113:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
²:@0.246788:0.187948:0.251156:0.187948:0.251156:0.175446:0.246788:0.175446:0.000000
x:@0.266883:0.187991:0.272655:0.187991:0.272655:0.175510:0.266883:0.175510:0.000000
y = ax²+bx+c:@0.215334:0.318183:0.287638:0.318183:0.287638:0.305703:0.215334:0.305703:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.291075:0.344811:0.297836:0.344811:0.297836:0.332309:0.291075:0.332309:0.000000
x:@0.309094:0.342467:0.319077:0.342467:0.319077:0.329987:0.309094:0.329987:0.000000:0.000000
x:@0.194636:0.343263:0.204620:0.343263:0.204620:0.330782:0.194636:0.330782:0.000000:0.000000
x:@0.352049:0.346843:0.357822:0.346843:0.357822:0.334362:0.352049:0.334362:0.000000
y:@0.286878:0.107162:0.292837:0.107162:0.292837:0.094682:0.286878:0.094682:0.000000
p:@0.302154:0.391265:0.313634:0.391265:0.313634:0.381240:0.302154:0.381240:0.000000
 Figura 3.14.:@0.313634:0.391972:0.370994:0.391972:0.370994:0.380496:0.313634:0.380496:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y=  x:@0.324850:0.739455:0.357707:0.739455:0.357707:0.726719:0.324850:0.726719:0.000000:0.000000:0.000000:0.000000:0.000000
α +β +λ:@0.342594:0.739586:0.400153:0.739586:0.400153:0.725293:0.342594:0.725293:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
²:@0.357707:0.739411:0.362165:0.739411:0.362165:0.726653:0.357707:0.726653:0.000000
x:@0.378214:0.739455:0.384104:0.739455:0.384104:0.726719:0.378214:0.726719:0.000000
y = ax²+bx+c:@0.181596:0.643403:0.255379:0.643403:0.255379:0.630667:0.181596:0.630667:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.289712:0.826599:0.296611:0.826599:0.296611:0.813841:0.289712:0.813841:0.000000
x:@0.397288:0.828672:0.403179:0.828672:0.403179:0.815936:0.397288:0.815936:0.000000
y:@0.285517:0.611514:0.291598:0.611514:0.291598:0.598778:0.285517:0.598778:0.000000
p:@0.349640:0.918638:0.361121:0.918638:0.361121:0.908613:0.349640:0.908613:0.000000
 Figura 3.15.:@0.361121:0.919345:0.418481:0.919345:0.418481:0.907869:0.361121:0.907869:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000