79:@0.921900:0.510692:0.940807:0.510692:0.940807:0.494068:0.921900:0.494068:0.000000:0.000000
2. :@0.120578:0.453055:0.139319:0.453055:0.139319:0.435919:0.120578:0.435919:0.000000:0.000000:0.000000
Factoriza:@0.153821:0.453055:0.222630:0.453055:0.222630:0.436431:0.153821:0.436431:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 las siguientes expresiones.:@0.222630:0.453055:0.418881:0.453055:0.418881:0.436666:0.222630:0.436666:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a) :@0.153821:0.487935:0.172544:0.487935:0.172544:0.471034:0.153821:0.471034:0.000000:0.000000:0.000000
x:@0.187065:0.487935:0.194528:0.487935:0.194528:0.471573:0.187065:0.471573:0.000000
2:@0.194523:0.481882:0.199766:0.481882:0.199766:0.472327:0.194523:0.472327:0.000000
 + 3  + 2 = :@0.199766:0.487930:0.282378:0.487930:0.282378:0.471541:0.199766:0.471541:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.227813:0.487930:0.235277:0.487930:0.235277:0.471568:0.227813:0.471568:0.000000
_________________________:@0.282378:0.487930:0.490610:0.487930:0.490610:0.471541:0.282378:0.471541:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b) :@0.153826:0.525742:0.173857:0.525742:0.173857:0.508841:0.153826:0.508841:0.000000:0.000000:0.000000
x:@0.187070:0.525742:0.194533:0.525742:0.194533:0.509380:0.187070:0.509380:0.000000
2:@0.194523:0.519689:0.199766:0.519689:0.199766:0.510135:0.194523:0.510135:0.000000
 +   – 2 = :@0.199766:0.525737:0.269497:0.525737:0.269497:0.509348:0.199766:0.509348:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.217973:0.525737:0.225436:0.525737:0.225436:0.509375:0.217973:0.509375:0.000000
___________________________:@0.269073:0.525737:0.493890:0.525737:0.493890:0.509348:0.269073:0.509348:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c) :@0.153826:0.563549:0.171462:0.563549:0.171462:0.546648:0.153826:0.546648:0.000000:0.000000:0.000000
x:@0.187070:0.563549:0.194533:0.563549:0.194533:0.547187:0.187070:0.547187:0.000000
2:@0.194523:0.557495:0.199766:0.557495:0.199766:0.547940:0.194523:0.547940:0.000000
 –   – 2 = :@0.199766:0.563542:0.269202:0.563542:0.269202:0.547154:0.199766:0.547154:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.216794:0.563542:0.224257:0.563542:0.224257:0.547181:0.216794:0.547181:0.000000
___________________________:@0.269073:0.563542:0.493890:0.563542:0.493890:0.547154:0.269073:0.547154:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d) :@0.153826:0.601354:0.173894:0.601354:0.173894:0.584454:0.153826:0.584454:0.000000:0.000000:0.000000
x:@0.187070:0.601354:0.194533:0.601354:0.194533:0.584993:0.187070:0.584993:0.000000
2:@0.194523:0.595301:0.199766:0.595301:0.199766:0.585746:0.194523:0.585746:0.000000
 – 3  + 2 = :@0.199766:0.601348:0.277844:0.601348:0.277844:0.584959:0.199766:0.584959:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.224939:0.601348:0.232402:0.601348:0.232402:0.584987:0.224939:0.584987:0.000000
__________________________:@0.277292:0.601348:0.493816:0.601348:0.493816:0.584959:0.277292:0.584959:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
e) :@0.153826:0.639160:0.172696:0.639160:0.172696:0.622260:0.153826:0.622260:0.000000:0.000000:0.000000
2  – 3  – 2 = :@0.187070:0.639160:0.279077:0.639155:0.279077:0.622766:0.187070:0.622771:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.196063:0.639160:0.203526:0.639160:0.203526:0.622799:0.196063:0.622799:0.000000
2:@0.203516:0.633108:0.208758:0.633108:0.208758:0.623553:0.203516:0.623553:0.000000
x:@0.231534:0.639155:0.238997:0.639155:0.238997:0.622794:0.231534:0.622794:0.000000
__________________________:@0.277327:0.639155:0.493851:0.639155:0.493851:0.622766:0.277327:0.622766:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f) :@0.153825:0.676967:0.170649:0.676967:0.170649:0.660067:0.153825:0.660067:0.000000:0.000000:0.000000
6  – 7  +2 = :@0.187068:0.676967:0.279004:0.676961:0.279004:0.660572:0.187068:0.660578:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.196061:0.676967:0.203524:0.676967:0.203524:0.660606:0.196061:0.660606:0.000000
2:@0.203516:0.670914:0.208758:0.670914:0.208758:0.661359:0.203516:0.661359:0.000000
x:@0.231755:0.676961:0.239218:0.676961:0.239218:0.660600:0.231755:0.660600:0.000000
__________________________:@0.277364:0.676961:0.493888:0.676961:0.493888:0.660572:0.277364:0.660572:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g) :@0.153825:0.714773:0.173745:0.714773:0.173745:0.697872:0.153825:0.697872:0.000000:0.000000:0.000000
15  + 16  – 15 = :@0.187068:0.714773:0.311510:0.714767:0.311510:0.698378:0.187068:0.698384:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.205054:0.714773:0.212517:0.714773:0.212517:0.698412:0.205054:0.698412:0.000000
2:@0.212508:0.708720:0.217751:0.708720:0.217751:0.699165:0.212508:0.699165:0.000000
x:@0.252763:0.714767:0.260226:0.714767:0.260226:0.698406:0.252763:0.698406:0.000000
______________________:@0.310496:0.714767:0.493851:0.714767:0.493851:0.698378:0.310496:0.698378:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h) :@0.153825:0.752579:0.173727:0.752579:0.173727:0.735678:0.153825:0.735678:0.000000:0.000000:0.000000
x:@0.187068:0.752579:0.194531:0.752579:0.194531:0.736218:0.187068:0.736218:0.000000
2:@0.194523:0.746525:0.199766:0.746525:0.199766:0.736970:0.194523:0.736970:0.000000
 + 6x + 9 = :@0.199765:0.752573:0.282818:0.752573:0.282818:0.736184:0.199765:0.736184:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
_________________________:@0.282818:0.752573:0.491050:0.752573:0.491050:0.736184:0.282818:0.736184:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i) :@0.153825:0.790385:0.167905:0.790385:0.167905:0.773484:0.153825:0.773484:0.000000:0.000000:0.000000
20  + 9  – 18 = :@0.187068:0.790385:0.307585:0.790380:0.307585:0.773991:0.187068:0.773996:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.205054:0.790385:0.212517:0.790385:0.212517:0.774023:0.205054:0.774023:0.000000
2:@0.212508:0.784332:0.217751:0.784332:0.217751:0.774778:0.212508:0.774778:0.000000
x:@0.245797:0.790380:0.253260:0.790380:0.253260:0.774018:0.245797:0.774018:0.000000
______________________:@0.307585:0.790380:0.490940:0.790380:0.490940:0.773991:0.307585:0.773991:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
j) :@0.153825:0.828192:0.168161:0.828192:0.168161:0.811291:0.153825:0.811291:0.000000:0.000000:0.000000
16  – 9 = :@0.187068:0.828192:0.261313:0.828185:0.261313:0.811797:0.187068:0.811803:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.205054:0.828192:0.212517:0.828192:0.212517:0.811830:0.205054:0.811830:0.000000
2:@0.212508:0.822138:0.217751:0.822138:0.217751:0.812583:0.212508:0.812583:0.000000
____________________________:@0.260723:0.828185:0.493833:0.828185:0.493833:0.811797:0.260723:0.811797:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
k) :@0.153825:0.865997:0.172566:0.865997:0.172566:0.849097:0.153825:0.849097:0.000000:0.000000:0.000000
–4  – 15  – 9 = :@0.187068:0.865997:0.306037:0.865991:0.306037:0.849602:0.187068:0.849609:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.205275:0.865997:0.212738:0.865997:0.212738:0.849636:0.205275:0.849636:0.000000
2:@0.212729:0.859944:0.217972:0.859944:0.217972:0.850389:0.212729:0.850389:0.000000
x:@0.253242:0.865991:0.260705:0.865991:0.260705:0.849630:0.253242:0.849630:0.000000
______________________:@0.306037:0.865991:0.489392:0.865991:0.489392:0.849602:0.306037:0.849602:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
l) :@0.153825:0.903803:0.167922:0.903803:0.167922:0.886903:0.153825:0.886903:0.000000:0.000000:0.000000
–2  + 3  + 9 = :@0.187068:0.903803:0.300582:0.903798:0.300582:0.887409:0.187068:0.887414:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.205275:0.903803:0.212738:0.903803:0.212738:0.887442:0.205275:0.887442:0.000000
2:@0.212729:0.897751:0.217972:0.897751:0.217972:0.888196:0.212729:0.888196:0.000000
x:@0.246018:0.903798:0.253481:0.903798:0.253481:0.887437:0.246018:0.887437:0.000000
______________________:@0.300582:0.903798:0.483937:0.903798:0.483937:0.887409:0.300582:0.887409:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3. :@0.514435:0.171013:0.533176:0.171013:0.533176:0.153877:0.514435:0.153877:0.000000:0.000000:0.000000
Encierra:@0.547679:0.171013:0.609688:0.171013:0.609688:0.154389:0.547679:0.154389:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 en un rectángulo la ecuación equi-:@0.609688:0.171013:0.884628:0.171013:0.884628:0.154624:0.609688:0.154624:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
valente a la dada y :@0.547679:0.187609:0.693441:0.187609:0.693441:0.171221:0.547679:0.171221:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
determina:@0.694971:0.187609:0.774707:0.187609:0.774707:0.170985:0.694971:0.170985:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 la solución en :@0.774707:0.187609:0.888645:0.187609:0.888645:0.171221:0.774707:0.171221:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
forma gráfica.:@0.547679:0.204206:0.647483:0.204206:0.647483:0.187817:0.547679:0.187817:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a) :@0.547679:0.239086:0.566401:0.239086:0.566401:0.222185:0.547679:0.222185:0.000000:0.000000:0.000000
x:@0.580922:0.239086:0.588385:0.239086:0.588385:0.222725:0.580922:0.222725:0.000000
2:@0.588382:0.233037:0.593625:0.233037:0.593625:0.223482:0.588382:0.223482:0.000000
 – 2  + 1 = 0:@0.593625:0.239085:0.683460:0.239085:0.683460:0.222696:0.593625:0.222696:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.619903:0.239085:0.627366:0.239085:0.627366:0.222723:0.619903:0.222723:0.000000
 :@0.547685:0.384455:0.551721:0.384455:0.551721:0.368066:0.547685:0.368066:0.000000
b) :@0.547679:0.417227:0.567709:0.417227:0.567709:0.400326:0.547679:0.400326:0.000000:0.000000:0.000000
2  – 18 = 0:@0.580922:0.417227:0.665935:0.417227:0.665935:0.400838:0.580922:0.400838:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.589915:0.417227:0.597378:0.417227:0.597378:0.400865:0.589915:0.400865:0.000000
2:@0.597375:0.411179:0.602617:0.411179:0.602617:0.401624:0.597375:0.401624:0.000000
 :@0.547685:0.626742:0.551721:0.626742:0.551721:0.610353:0.547685:0.610353:0.000000
c) :@0.547679:0.659521:0.565314:0.659521:0.565314:0.642620:0.547679:0.642620:0.000000:0.000000:0.000000
–  + 4  + 5 = 0:@0.580922:0.659521:0.694443:0.659521:0.694443:0.643132:0.580922:0.643132:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.590136:0.659521:0.597599:0.659521:0.597599:0.643160:0.590136:0.643160:0.000000
2:@0.597596:0.653474:0.602838:0.653474:0.602838:0.643919:0.597596:0.643919:0.000000
x:@0.630886:0.659521:0.638349:0.659521:0.638349:0.643160:0.630886:0.643160:0.000000
 :@0.547685:0.911798:0.551721:0.911798:0.551721:0.895410:0.547685:0.895410:0.000000
1. :@0.120578:0.171017:0.139319:0.171017:0.139319:0.153881:0.120578:0.153881:0.000000:0.000000:0.000000
Busca:@0.153821:0.171017:0.198398:0.171017:0.198398:0.154393:0.153821:0.154393:0.000000:0.000000:0.000000:0.000000:0.000000
 los números   y   que completen cada :@0.198398:0.171017:0.497956:0.171017:0.497956:0.154628:0.198398:0.154628:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.299013:0.171017:0.335278:0.171017:0.335278:0.154656:0.299013:0.154656:0.000000:0.000000:0.000000
fila de la siguiente tabla.:@0.153821:0.187613:0.329822:0.187613:0.329822:0.171224:0.153821:0.171224:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.120578:0.424443:0.124300:0.424443:0.124300:0.407308:0.120578:0.407308:0.000000
a:@0.191921:0.215587:0.200968:0.215587:0.200968:0.200223:0.191921:0.200223:0.000000
b:@0.276286:0.215587:0.285416:0.215587:0.285416:0.200223:0.276286:0.200223:0.000000
a + b:@0.348121:0.215587:0.382413:0.215587:0.382413:0.200223:0.348121:0.200223:0.000000:0.000000:0.000000:0.000000:0.000000
a • b:@0.434932:0.215587:0.464416:0.215587:0.464416:0.200223:0.434932:0.200223:0.000000:0.000000:0.000000:0.000000:0.000000
 2:@0.369932:0.241424:0.381776:0.241424:0.381776:0.226525:0.369932:0.226525:0.000000:0.000000
1:@0.458016:0.241424:0.466192:0.241424:0.466192:0.226525:0.458016:0.226525:0.000000
–2:@0.365225:0.266369:0.381776:0.266369:0.381776:0.251470:0.365225:0.251470:0.000000:0.000000
–3:@0.449640:0.266369:0.466192:0.266369:0.466192:0.251470:0.449640:0.251470:0.000000:0.000000
 7:@0.369932:0.291314:0.381776:0.291314:0.381776:0.276415:0.369932:0.276415:0.000000:0.000000
–18:@0.441465:0.291314:0.466192:0.291314:0.466192:0.276415:0.441465:0.276415:0.000000:0.000000:0.000000
–7:@0.365225:0.316259:0.381776:0.316259:0.381776:0.301360:0.365225:0.301360:0.000000:0.000000
–18:@0.441465:0.316259:0.466192:0.316259:0.466192:0.301360:0.441465:0.301360:0.000000:0.000000:0.000000
–9:@0.365225:0.341204:0.381776:0.341204:0.381776:0.326305:0.365225:0.326305:0.000000:0.000000
 20:@0.446172:0.341204:0.466192:0.341204:0.466192:0.326305:0.446172:0.326305:0.000000:0.000000:0.000000
–3:@0.365225:0.366149:0.381776:0.366149:0.381776:0.351250:0.365225:0.351250:0.000000:0.000000
2:@0.458016:0.366149:0.466192:0.366149:0.466192:0.351250:0.458016:0.351250:0.000000
 2:@0.369932:0.391094:0.381776:0.391094:0.381776:0.376195:0.369932:0.376195:0.000000:0.000000
–35:@0.441465:0.391094:0.466192:0.391094:0.466192:0.376195:0.441465:0.376195:0.000000:0.000000:0.000000
–5:@0.365225:0.416038:0.381776:0.416038:0.381776:0.401139:0.365225:0.401139:0.000000:0.000000
–24:@0.441465:0.416038:0.466192:0.416038:0.466192:0.401139:0.441465:0.401139:0.000000:0.000000:0.000000
Taller:@0.179762:0.130414:0.240657:0.130414:0.240657:0.096466:0.179762:0.096466:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
I.M.4.3.5. Plantea y resuelve problemas que involucren ecuaciones de segundo grado y la aplicación de las propiedades de las raíces de :@0.260784:0.113160:0.881546:0.113160:0.881546:0.102730:0.260784:0.102730:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la ecuación de segundo grado; juzga la validez de las soluciones obtenidas en el contexto del problema.:@0.260784:0.123721:0.745980:0.123721:0.745980:0.113292:0.260784:0.113292:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(  + 1) = 0:@0.797321:0.295942:0.870645:0.295942:0.870645:0.279553:0.797321:0.279553:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.802204:0.295942:0.809668:0.295942:0.809668:0.279581:0.802204:0.279581:0.000000
(  – 9) = 0:@0.760945:0.518707:0.841055:0.518715:0.841055:0.502326:0.760945:0.502318:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.765828:0.518707:0.776608:0.518707:0.776608:0.502346:0.765828:0.502346:0.000000:0.000000
2:@0.776605:0.512666:0.781848:0.512666:0.781848:0.503111:0.776605:0.503111:0.000000
(  + 3)(  – 3)= 0:@0.760950:0.542434:0.873746:0.542434:0.873746:0.526045:0.760950:0.526045:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.765833:0.542434:0.773297:0.542434:0.773297:0.526072:0.765833:0.526072:0.000000
x:@0.811110:0.542434:0.818573:0.542434:0.818573:0.526072:0.811110:0.526072:0.000000
( + 1)(  – 5) = 0:@0.757559:0.693308:0.873672:0.693308:0.873672:0.676920:0.757559:0.676920:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.762443:0.693308:0.773223:0.693308:0.773223:0.676947:0.762443:0.676947:0.000000:0.000000
x:@0.807001:0.693308:0.814464:0.693308:0.814464:0.676947:0.807001:0.676947:0.000000
(  – 1)(  + 5) = 0:@0.757559:0.717027:0.874391:0.717027:0.874391:0.700639:0.757559:0.700639:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.762443:0.717027:0.769906:0.717027:0.769906:0.700666:0.762443:0.700666:0.000000
x:@0.805950:0.717027:0.813413:0.717027:0.813413:0.700666:0.805950:0.700666:0.000000
y:@0.668222:0.260026:0.673663:0.260026:0.673663:0.248127:0.668222:0.248127:0.000000
x:@0.766874:0.337013:0.772301:0.337013:0.772301:0.325114:0.766874:0.325114:0.000000
3:@0.652126:0.279187:0.658667:0.279187:0.658667:0.267268:0.652126:0.267268:0.000000
3:@0.743782:0.351105:0.750322:0.351105:0.750322:0.339186:0.743782:0.339186:0.000000
2:@0.652126:0.300662:0.658667:0.300662:0.658667:0.288743:0.652126:0.288743:0.000000
2:@0.715759:0.351105:0.722299:0.351105:0.722299:0.339186:0.715759:0.339186:0.000000
1:@0.652126:0.322046:0.658667:0.322046:0.658667:0.310127:0.652126:0.310127:0.000000
–1 0:@0.629330:0.351105:0.659739:0.351105:0.659739:0.339186:0.629330:0.339186:0.000000:0.000000:0.000000:0.000000
1:@0.689518:0.351105:0.696058:0.351105:0.696058:0.339186:0.689518:0.339186:0.000000
y:@0.698376:0.441095:0.703818:0.441095:0.703818:0.429196:0.698376:0.429196:0.000000
y:@0.698658:0.681129:0.704099:0.681129:0.704099:0.669230:0.698658:0.669230:0.000000
x:@0.799172:0.470848:0.804600:0.470848:0.804600:0.458949:0.799172:0.458949:0.000000
x:@0.799454:0.756245:0.804881:0.756245:0.804881:0.744346:0.799454:0.744346:0.000000
5:@0.742589:0.486147:0.749130:0.486147:0.749130:0.474228:0.742589:0.474228:0.000000
5:@0.742871:0.771544:0.749411:0.771544:0.749411:0.759625:0.742871:0.759625:0.000000
5:@0.677335:0.721403:0.683876:0.721403:0.683876:0.709484:0.677335:0.709484:0.000000
–5:@0.626917:0.486147:0.640159:0.486147:0.640159:0.474228:0.626917:0.474228:0.000000:0.000000
–5:@0.627199:0.771544:0.640440:0.771544:0.640440:0.759625:0.627199:0.759625:0.000000:0.000000
–5:@0.671090:0.521562:0.684331:0.521562:0.684331:0.509643:0.671090:0.509643:0.000000:0.000000
–5:@0.671372:0.806960:0.684613:0.806960:0.684613:0.795040:0.671372:0.795040:0.000000:0.000000
–10:@0.667820:0.563627:0.687601:0.563627:0.687601:0.551707:0.667820:0.551707:0.000000:0.000000:0.000000
–10:@0.668102:0.849024:0.687883:0.849024:0.687883:0.837105:0.668102:0.837105:0.000000:0.000000:0.000000
–15:@0.667820:0.606375:0.687601:0.606375:0.687601:0.594456:0.667820:0.594456:0.000000:0.000000:0.000000
0:@0.680136:0.486147:0.686677:0.486147:0.686677:0.474228:0.680136:0.474228:0.000000
0:@0.680418:0.771544:0.686958:0.771544:0.686958:0.759625:0.680418:0.759625:0.000000
(  – 1)  = 0:@0.797123:0.270424:0.871191:0.270424:0.871191:0.254035:0.797123:0.254035:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.801749:0.270424:0.809212:0.270424:0.809212:0.254063:0.801749:0.254063:0.000000
2:@0.838825:0.264377:0.844068:0.264377:0.844068:0.254822:0.838825:0.254822:0.000000
1:@0.193580:0.240471:0.202572:0.240471:0.202572:0.224082:0.193580:0.224082:0.000000
–3:@0.184624:0.265615:0.202572:0.265615:0.202572:0.249226:0.184624:0.249226:0.000000:0.000000
9:@0.193580:0.290758:0.202572:0.290758:0.202572:0.274369:0.193580:0.274369:0.000000
2:@0.193580:0.315902:0.202572:0.315902:0.202572:0.299513:0.193580:0.299513:0.000000
–4:@0.184624:0.341045:0.202572:0.341045:0.202572:0.324656:0.184624:0.324656:0.000000:0.000000
–2:@0.184624:0.366189:0.202572:0.366189:0.202572:0.349800:0.184624:0.349800:0.000000:0.000000
7:@0.193580:0.391332:0.202572:0.391332:0.202572:0.374944:0.193580:0.374944:0.000000
–8:@0.184624:0.416476:0.202572:0.416476:0.202572:0.400087:0.184624:0.400087:0.000000:0.000000
1:@0.279010:0.240458:0.288003:0.240458:0.288003:0.224069:0.279010:0.224069:0.000000
1:@0.279010:0.265601:0.288003:0.265601:0.288003:0.249212:0.279010:0.249212:0.000000
–2:@0.270055:0.290745:0.288003:0.290745:0.288003:0.274356:0.270055:0.274356:0.000000:0.000000
–9:@0.270055:0.315888:0.288003:0.315888:0.288003:0.299499:0.270055:0.299499:0.000000:0.000000
–5:@0.270055:0.341032:0.288003:0.341032:0.288003:0.324643:0.270055:0.324643:0.000000:0.000000
–1:@0.270055:0.366175:0.288003:0.366175:0.288003:0.349786:0.270055:0.349786:0.000000:0.000000
–5:@0.270055:0.391319:0.288003:0.391319:0.288003:0.374930:0.270055:0.374930:0.000000:0.000000
3:@0.279010:0.416462:0.288003:0.416462:0.288003:0.400073:0.279010:0.400073:0.000000
(  + 1)(  + 2):@0.289072:0.487011:0.376271:0.487011:0.376271:0.470622:0.289072:0.470622:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.293697:0.487011:0.301160:0.487011:0.301160:0.470649:0.293697:0.470649:0.000000
x:@0.337168:0.487011:0.344631:0.487011:0.344631:0.470649:0.337168:0.470649:0.000000
Solución:   =   = 1 :@0.609031:0.381471:0.751768:0.381504:0.751768:0.365115:0.609031:0.365082:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.677582:0.381471:0.685045:0.381471:0.685045:0.365110:0.677582:0.365110:0.000000
1:@0.684790:0.384668:0.690033:0.384668:0.690033:0.375113:0.684790:0.375113:0.000000
x:@0.708163:0.381504:0.715626:0.381504:0.715626:0.365143:0.708163:0.365143:0.000000
2:@0.715367:0.384668:0.720609:0.384668:0.720609:0.375113:0.715367:0.375113:0.000000
Solución:   = –3,    = 3:@0.714636:0.621820:0.881519:0.621820:0.881519:0.605431:0.714636:0.605431:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.783187:0.621820:0.790650:0.621820:0.790650:0.605458:0.783187:0.605458:0.000000
1:@0.790384:0.624983:0.795627:0.624983:0.795627:0.615428:0.790384:0.615428:0.000000
x:@0.841950:0.621820:0.849413:0.621820:0.849413:0.605458:0.841950:0.605458:0.000000
2:@0.849155:0.624983:0.854397:0.624983:0.854397:0.615428:0.849155:0.615428:0.000000
Solución:   = –1,    = 5:@0.714620:0.905728:0.881519:0.905722:0.881519:0.889333:0.714620:0.889339:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.783170:0.905728:0.790634:0.905728:0.790634:0.889367:0.783170:0.889367:0.000000
1:@0.790384:0.908886:0.795627:0.908886:0.795627:0.899331:0.790384:0.899331:0.000000
x:@0.841950:0.905722:0.849413:0.905722:0.849413:0.889361:0.841950:0.889361:0.000000
2:@0.849155:0.908886:0.854397:0.908886:0.854397:0.899331:0.849155:0.899331:0.000000
(  – 1)(  + 2):@0.275655:0.525333:0.361085:0.525333:0.361085:0.508944:0.275655:0.508944:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.280280:0.525333:0.287743:0.525333:0.287743:0.508972:0.280280:0.508972:0.000000
x:@0.321982:0.525333:0.329445:0.525333:0.329445:0.508972:0.321982:0.508972:0.000000
(  + 1)(  – 2):@0.275655:0.563159:0.361085:0.563159:0.361085:0.546770:0.275655:0.546770:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.280280:0.563159:0.287743:0.563159:0.287743:0.546798:0.280280:0.546798:0.000000
x:@0.323751:0.563159:0.331214:0.563159:0.331214:0.546798:0.323751:0.546798:0.000000
(  – 1)(  – 2):@0.285716:0.601455:0.369378:0.601455:0.369378:0.585066:0.285716:0.585066:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.290342:0.601455:0.297805:0.601455:0.297805:0.585094:0.290342:0.585094:0.000000
x:@0.332043:0.601455:0.339507:0.601455:0.339507:0.585094:0.332043:0.585094:0.000000
(2  + 1)(  – 2):@0.283192:0.639170:0.377357:0.639170:0.377357:0.622781:0.283192:0.622781:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.296552:0.639170:0.304015:0.639170:0.304015:0.622809:0.296552:0.622809:0.000000
x:@0.340023:0.639170:0.347486:0.639170:0.347486:0.622809:0.340023:0.622809:0.000000
(2  – 1)(3  – 2):@0.285698:0.677466:0.386829:0.677466:0.386829:0.661078:0.285698:0.661078:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.299058:0.677466:0.306521:0.677466:0.306521:0.661105:0.299058:0.661105:0.000000
x:@0.349494:0.677466:0.356958:0.677466:0.356958:0.661105:0.349494:0.661105:0.000000
–(4  + 3)(  + 3):@0.315293:0.865490:0.420183:0.865490:0.420183:0.849101:0.315293:0.849101:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.337609:0.865490:0.345072:0.865490:0.345072:0.849128:0.337609:0.849128:0.000000
x:@0.381079:0.865490:0.388543:0.865490:0.388543:0.849128:0.381079:0.849128:0.000000
(2  + 3)(–   + 3):@0.308548:0.903896:0.417216:0.903896:0.417216:0.887507:0.308548:0.887507:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.321908:0.903896:0.329371:0.903896:0.329371:0.887535:0.321908:0.887535:0.000000
x:@0.378112:0.903896:0.385576:0.903896:0.385576:0.887535:0.378112:0.887535:0.000000
(5  – 3)(3  + 5):@0.315459:0.714615:0.418358:0.714615:0.418358:0.698226:0.315459:0.698226:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.328819:0.714615:0.336282:0.714615:0.336282:0.698253:0.328819:0.698253:0.000000
x:@0.379255:0.714615:0.386718:0.714615:0.386718:0.698253:0.379255:0.698253:0.000000
(4  – 3)(5  + 6):@0.313782:0.790059:0.416682:0.790059:0.416682:0.773670:0.313782:0.773670:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.327142:0.790059:0.334605:0.790059:0.334605:0.773698:0.327142:0.773698:0.000000
x:@0.377578:0.790059:0.385041:0.790059:0.385041:0.773698:0.377578:0.773698:0.000000
(4  – 3)(4  + 3):@0.267270:0.828355:0.370170:0.828355:0.370170:0.811966:0.267270:0.811966:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.280630:0.828355:0.288093:0.828355:0.288093:0.811994:0.280630:0.811994:0.000000
x:@0.331067:0.828355:0.338530:0.828355:0.338530:0.811994:0.331067:0.811994:0.000000
(  + 3):@0.291558:0.753021:0.335287:0.753021:0.335287:0.736633:0.291558:0.736633:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.296183:0.753021:0.303646:0.753021:0.303646:0.736660:0.296183:0.736660:0.000000
2:@0.335047:0.746968:0.340290:0.746968:0.340290:0.737413:0.335047:0.737413:0.000000
A:@0.717561:0.336147:0.728341:0.336147:0.728341:0.319758:0.717561:0.319758:0.000000
(–3, 0):@0.660114:0.470365:0.691139:0.470365:0.691139:0.458446:0.660114:0.458446:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(–1, 0):@0.640024:0.755762:0.671050:0.755762:0.671050:0.743843:0.640024:0.743843:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(3, 0):@0.729388:0.470365:0.753901:0.470365:0.753901:0.458446:0.729388:0.458446:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(5, 0):@0.749719:0.755762:0.774231:0.755762:0.774231:0.743843:0.749719:0.743843:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 ©:@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 :@0.079553:0.684192:0.079553:0.268045:0.061505:0.268045:0.061505:0.684192:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000