122:@0.026565:0.967627:0.050760:0.967627:0.050760:0.951847:0.026565:0.951847:0.000000:0.000000:0.000000
Ecuación de segundo grado:@0.404235:0.112163:0.737490:0.112163:0.737490:0.067503:0.404235:0.067503:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.1.26. Aplicar las propiedades de las raíces de la ecuación de segundo grado en la factorización de la función cuadrática.:@0.143847:0.951046:0.673356:0.951046:0.673356:0.941004:0.143847:0.941004:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean  ,  ,   :@0.404238:0.136894:0.491240:0.136894:0.491240:0.120397:0.404238:0.120397:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b c:@0.443982:0.137010:0.487098:0.137010:0.487098:0.120541:0.443982:0.120541:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.493186:0.136677:0.509234:0.136677:0.509234:0.122030:0.493186:0.122030:0.000000
R:@0.509234:0.135926:0.523143:0.135926:0.523143:0.122479:0.509234:0.122479:0.000000
 con  ≠ 0 y   la función de   en  , definida por :@0.523143:0.136894:0.895824:0.136894:0.895824:0.120397:0.523143:0.120397:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a :@0.562271:0.137010:0.575390:0.137010:0.575390:0.120541:0.562271:0.120541:0.000000:0.000000
f:@0.622744:0.137010:0.627041:0.137010:0.627041:0.120541:0.622744:0.120541:0.000000
R:@0.735885:0.135926:0.749795:0.135926:0.749795:0.122479:0.735885:0.122479:0.000000
R:@0.779521:0.135926:0.793431:0.135926:0.793431:0.122479:0.779521:0.122479:0.000000
+:@0.479039:0.156767:0.489616:0.156767:0.489616:0.140486:0.479039:0.140486:0.000000
+:@0.510827:0.156767:0.521403:0.156767:0.521403:0.140486:0.510827:0.140486:0.000000
∀∈:@0.544117:0.156767:0.583148:0.156767:0.583148:0.140486:0.544117:0.140486:0.000000:0.000000
() =:@0.415753:0.156131:0.450008:0.156131:0.450008:0.139633:0.415753:0.139633:0.000000:0.000000:0.000000:0.000000
,:@0.532444:0.156131:0.535199:0.156131:0.535199:0.139633:0.532444:0.139633:0.000000
2:@0.470401:0.148094:0.475319:0.148094:0.475319:0.138545:0.470401:0.138545:0.000000
fx:@0.408627:0.156247:0.429915:0.156247:0.429915:0.139778:0.408627:0.139778:0.000000:0.000000
ax:@0.452918:0.156247:0.469178:0.156247:0.469178:0.139778:0.452918:0.139778:0.000000:0.000000
bx c:@0.491545:0.156247:0.530923:0.156247:0.530923:0.139778:0.491545:0.139778:0.000000:0.000000:0.000000:0.000000
x:@0.557721:0.156247:0.565196:0.156247:0.565196:0.139778:0.557721:0.139778:0.000000
. Consideremos la ecuación: para :@0.601623:0.156131:0.848368:0.156131:0.848368:0.139633:0.601623:0.139633:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
hallar:@0.851239:0.156247:0.891773:0.156247:0.891773:0.139778:0.851239:0.139778:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  :@0.891777:0.156131:0.895919:0.156131:0.895919:0.139633:0.891777:0.139633:0.000000:0.000000
x:@0.404250:0.173597:0.411725:0.173597:0.411725:0.157129:0.404250:0.157129:0.000000
:@0.411725:0.173265:0.427773:0.173265:0.427773:0.158618:0.411725:0.158618:0.000000
R:@0.427773:0.172513:0.441682:0.172513:0.441682:0.159066:0.427773:0.159066:0.000000
   :@0.441682:0.173482:0.468269:0.173482:0.468269:0.156984:0.441682:0.156984:0.000000:0.000000:0.000000
tal que f  x:@0.445825:0.173597:0.519803:0.173597:0.519803:0.157129:0.445825:0.157129:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  ( ) = 0, que se escribe como sigue::@0.493795:0.173482:0.748690:0.173482:0.748690:0.156984:0.493795:0.156984:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
hallar:@0.521995:0.192718:0.559794:0.192718:0.559794:0.176221:0.521995:0.176221:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tal que:@0.611560:0.192718:0.659270:0.192718:0.659270:0.176221:0.611560:0.176221:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=0.:@0.747948:0.192718:0.772782:0.192718:0.772782:0.176221:0.747948:0.176221:0.000000:0.000000:0.000000
2:@0.680673:0.184682:0.685590:0.184682:0.685590:0.175133:0.680673:0.175133:0.000000
∈:@0.578798:0.193355:0.592534:0.193355:0.592534:0.177074:0.578798:0.177074:0.000000
+:@0.690421:0.193355:0.700997:0.193355:0.700997:0.177074:0.690421:0.177074:0.000000
+:@0.723810:0.193355:0.734387:0.193355:0.734387:0.177074:0.723810:0.177074:0.000000
x:@0.567588:0.192834:0.575063:0.192834:0.575063:0.176365:0.567588:0.176365:0.000000
ax:@0.663182:0.192834:0.679442:0.192834:0.679442:0.176365:0.663182:0.176365:0.000000:0.000000
bxc:@0.703697:0.192834:0.744693:0.192834:0.744693:0.176365:0.703697:0.176365:0.000000:0.000000:0.000000
Esta ecuación se llama ecuación de segundo grado, donde   es la in-:@0.404238:0.216356:0.891761:0.216356:0.891761:0.199858:0.404238:0.199858:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.825565:0.216471:0.833040:0.216471:0.833040:0.200003:0.825565:0.200003:0.000000
cógnita. En la práctica, esta ecuación surge en muchas aplicaciones, :@0.404238:0.233706:0.895937:0.233706:0.895937:0.217209:0.404238:0.217209:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
por lo que es importante saber las condiciones bajo las cuales tiene :@0.404238:0.251057:0.895995:0.251057:0.895995:0.234560:0.404238:0.234560:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
soluciones reales y cómo calcularlas, además de conocer las condicio-:@0.404238:0.268408:0.891759:0.268408:0.891759:0.251910:0.404238:0.251910:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nes para las que la ecuación no tiene soluciones reales.:@0.404238:0.285759:0.789959:0.285759:0.789959:0.269261:0.404238:0.269261:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejercicios resueltos:@0.404238:0.310614:0.534893:0.310614:0.534893:0.293827:0.404238:0.293827:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.:@0.404238:0.336813:0.416510:0.336813:0.416510:0.320099:0.404238:0.320099:0.000000:0.000000
   Sea  ()=107:@0.416510:0.336596:0.541412:0.336601:0.541412:0.320104:0.416510:0.320099:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−+:@0.520412:0.337238:0.560311:0.337238:0.560311:0.320957:0.520412:0.320957:0.000000:0.000000
∀∈:@0.588669:0.337238:0.625697:0.337238:0.625697:0.320957:0.588669:0.320957:0.000000:0.000000
,:@0.577004:0.336601:0.579759:0.336601:0.579759:0.320104:0.577004:0.320104:0.000000
.  Los números reales   = 2 y   = 5 :@0.644066:0.336601:0.895928:0.336601:0.895928:0.320104:0.644066:0.320104:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.568942:0.328566:0.573860:0.328566:0.573860:0.319017:0.568942:0.319017:0.000000
Pt:@0.459109:0.336717:0.479491:0.336717:0.479491:0.320248:0.459109:0.320248:0.000000:0.000000
tt:@0.541660:0.336717:0.567900:0.336717:0.567900:0.320248:0.541660:0.320248:0.000000:0.000000
t:@0.602288:0.336717:0.607952:0.336717:0.607952:0.320248:0.602288:0.320248:0.000000
r:@0.796322:0.336717:0.802352:0.336717:0.802352:0.320248:0.796322:0.320248:0.000000
1:@0.802325:0.339335:0.806622:0.339335:0.806622:0.330569:0.802325:0.330569:0.000000
r:@0.852705:0.336717:0.858735:0.336717:0.858735:0.320248:0.852705:0.320248:0.000000
2:@0.858707:0.339335:0.863004:0.339335:0.863004:0.330569:0.858707:0.330569:0.000000
 :@0.891767:0.336601:0.895909:0.336601:0.895909:0.320104:0.891767:0.320104:0.000000
son raíces del polinomio o función  . :@0.427686:0.353952:0.694236:0.353952:0.694236:0.337455:0.427686:0.337455:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P:@0.678555:0.354068:0.687339:0.354068:0.687339:0.337599:0.678555:0.337599:0.000000
 :@0.404240:0.371925:0.408382:0.371925:0.408382:0.355427:0.404240:0.355427:0.000000
En efecto,  :@0.427686:0.371925:0.504996:0.371925:0.504996:0.355427:0.427686:0.355427:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(2)=10 72 2= 0,:@0.517074:0.373779:0.676541:0.373779:0.676541:0.356796:0.517074:0.356796:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.640323:0.365507:0.645385:0.365507:0.645385:0.355677:0.640323:0.355677:0.000000
P:@0.507642:0.373898:0.516685:0.373898:0.516685:0.356945:0.507642:0.356945:0.000000
−:@0.573345:0.374434:0.584232:0.374434:0.584232:0.357674:0.573345:0.357674:0.000000
+:@0.618284:0.374434:0.629171:0.374434:0.629171:0.357674:0.618284:0.357674:0.000000
×:@0.596778:0.373660:0.605772:0.373660:0.605772:0.359815:0.596778:0.359815:0.000000
 :@0.680902:0.371932:0.685044:0.371932:0.685044:0.355434:0.680902:0.355434:0.000000
(5)=10 75 5= 0.:@0.697239:0.373990:0.855743:0.373990:0.855743:0.356833:0.697239:0.356833:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.819143:0.365633:0.824257:0.365633:0.824257:0.355703:0.819143:0.355703:0.000000
P:@0.687712:0.374111:0.696848:0.374111:0.696848:0.356983:0.687712:0.356983:0.000000
−:@0.753209:0.374652:0.764209:0.374652:0.764209:0.357720:0.753209:0.357720:0.000000
+:@0.797749:0.374652:0.808749:0.374652:0.808749:0.357720:0.797749:0.357720:0.000000
×:@0.776893:0.373870:0.785980:0.373870:0.785980:0.359883:0.776893:0.359883:0.000000
  :@0.859268:0.371932:0.867552:0.371932:0.867552:0.355434:0.859268:0.355434:0.000000:0.000000
2.:@0.404242:0.398507:0.416514:0.398507:0.416514:0.381793:0.404242:0.381793:0.000000:0.000000
   Los polinomios siguientes,  ()=:@0.416514:0.398290:0.660017:0.398296:0.660017:0.381798:0.416514:0.381793:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.677856:0.398932:0.688433:0.398932:0.688433:0.382651:0.677856:0.382651:0.000000
∀ ∈:@0.709162:0.398932:0.746190:0.398932:0.746190:0.382651:0.709162:0.382651:0.000000:0.000000:0.000000
1,:@0.689570:0.398296:0.700243:0.398296:0.700243:0.381798:0.689570:0.381798:0.000000:0.000000
,  :@0.765283:0.398296:0.775445:0.398296:0.775445:0.381798:0.765283:0.381798:0.000000:0.000000:0.000000
2:@0.669219:0.390260:0.674136:0.390260:0.674136:0.380711:0.669219:0.380711:0.000000
Pt:@0.619746:0.398412:0.640128:0.398412:0.640128:0.381943:0.619746:0.381943:0.000000:0.000000
t:@0.662518:0.398412:0.668182:0.398412:0.668182:0.381943:0.662518:0.381943:0.000000
t:@0.722780:0.398412:0.728444:0.398412:0.728444:0.381943:0.722780:0.381943:0.000000
++:@0.489477:0.418169:0.520629:0.418169:0.520629:0.401888:0.489477:0.401888:0.000000:0.000000
∀∈:@0.542457:0.418169:0.579485:0.418169:0.579485:0.401888:0.542457:0.401888:0.000000:0.000000
()=:@0.440524:0.417533:0.471638:0.417533:0.471638:0.401035:0.440524:0.401035:0.000000:0.000000:0.000000
1,:@0.521766:0.417533:0.533537:0.417533:0.533537:0.401035:0.521766:0.401035:0.000000:0.000000
,  :@0.598577:0.417533:0.608582:0.417533:0.608582:0.401035:0.598577:0.401035:0.000000:0.000000:0.000000
2:@0.480838:0.409497:0.485756:0.409497:0.485756:0.399948:0.480838:0.399948:0.000000
Qt:@0.427755:0.417648:0.451740:0.417648:0.451740:0.401180:0.427755:0.401180:0.000000:0.000000
t:@0.474137:0.417648:0.479801:0.417648:0.479801:0.401180:0.474137:0.401180:0.000000
t:@0.501995:0.417648:0.507659:0.417648:0.507659:0.401180:0.501995:0.401180:0.000000
t:@0.556072:0.417648:0.561736:0.417648:0.561736:0.401180:0.556072:0.401180:0.000000
−+:@0.670507:0.418765:0.703786:0.418765:0.703786:0.402015:0.670507:0.402015:0.000000:0.000000
∀∈:@0.730069:0.418765:0.767907:0.418765:0.767907:0.402015:0.730069:0.402015:0.000000:0.000000
Rt:@0.609578:0.418229:0.630548:0.418229:0.630548:0.401286:0.609578:0.401286:0.000000:0.000000
t:@0.653897:0.418229:0.659725:0.418229:0.659725:0.401286:0.653897:0.401286:0.000000
t:@0.683946:0.418229:0.689773:0.418229:0.689773:0.401286:0.683946:0.401286:0.000000
t:@0.744063:0.418229:0.749890:0.418229:0.749890:0.401286:0.744063:0.401286:0.000000
() =:@0.618993:0.418111:0.651162:0.418111:0.651162:0.401137:0.618993:0.401137:0.000000:0.000000:0.000000:0.000000
2,:@0.706343:0.418111:0.719366:0.418111:0.719366:0.401137:0.706343:0.401137:0.000000:0.000000
2:@0.660813:0.409843:0.665872:0.409843:0.665872:0.400018:0.660813:0.400018:0.000000
 no tienen :@0.783023:0.417533:0.859699:0.417533:0.859699:0.401035:0.783023:0.401035:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
raíces en el conjunto  , pues para todo :@0.427695:0.434883:0.711736:0.434883:0.711736:0.418386:0.427695:0.418386:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.578443:0.433915:0.592353:0.433915:0.592353:0.420468:0.578443:0.420468:0.000000
t:@0.711736:0.434999:0.717400:0.434999:0.717400:0.418530:0.711736:0.418530:0.000000
:@0.717400:0.434667:0.733448:0.434667:0.733448:0.420020:0.717400:0.420020:0.000000
R:@0.733448:0.433915:0.747357:0.433915:0.747357:0.420468:0.733448:0.420468:0.000000
,   + 1 > 0,  :@0.747357:0.434883:0.831083:0.434883:0.831083:0.418386:0.747357:0.418386:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.754254:0.434999:0.759918:0.434999:0.759918:0.418530:0.754254:0.418530:0.000000
2:@0.759915:0.428532:0.764868:0.428532:0.764868:0.418914:0.759915:0.418914:0.000000
t:@0.427688:0.452350:0.433352:0.452350:0.433352:0.435881:0.427688:0.435881:0.000000
2:@0.433355:0.445882:0.438308:0.445882:0.438308:0.436264:0.433355:0.436264:0.000000
 +   + 1 > 0,    –   + 2 > 0. Así,   ( ) ≠ 0,  ( ) ≠ 0,   ( ) ≠ 0, para :@0.438309:0.452234:0.885587:0.452234:0.885587:0.435737:0.438309:0.435737:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.457401:0.452350:0.463065:0.452350:0.463065:0.435881:0.457401:0.435881:0.000000
t:@0.529279:0.452350:0.534943:0.452350:0.534943:0.435881:0.529279:0.435881:0.000000
2:@0.534942:0.445882:0.539895:0.445882:0.539895:0.436264:0.534942:0.436264:0.000000
t:@0.558677:0.452350:0.564341:0.452350:0.564341:0.435881:0.558677:0.435881:0.000000
P t:@0.659666:0.452350:0.680068:0.452350:0.680068:0.435881:0.659666:0.435881:0.000000:0.000000:0.000000
Q t:@0.720506:0.452350:0.744009:0.452350:0.744009:0.435881:0.720506:0.435881:0.000000:0.000000:0.000000
R t:@0.788589:0.452350:0.809781:0.452350:0.809781:0.435881:0.788589:0.435881:0.000000:0.000000:0.000000
todo :@0.427693:0.469585:0.466955:0.469585:0.466955:0.453087:0.427693:0.453087:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.466955:0.469701:0.472619:0.469701:0.472619:0.453232:0.466955:0.453232:0.000000
:@0.472619:0.469368:0.488667:0.469368:0.488667:0.454721:0.472619:0.454721:0.000000
R:@0.488667:0.468616:0.502577:0.468616:0.502577:0.455169:0.488667:0.455169:0.000000
.:@0.502577:0.469585:0.505332:0.469585:0.505332:0.453087:0.502577:0.453087:0.000000
 :@0.404247:0.486936:0.408389:0.486936:0.408389:0.470438:0.404247:0.470438:0.000000
  Resolvemos en   la ecuación :@0.427701:0.486936:0.642000:0.486936:0.642000:0.470438:0.427701:0.470438:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.538796:0.485967:0.552705:0.485967:0.552705:0.472520:0.538796:0.472520:0.000000
ax:@0.642443:0.487051:0.658914:0.487051:0.658914:0.470583:0.642443:0.470583:0.000000:0.000000
2:@0.658909:0.480584:0.663863:0.480584:0.663863:0.470966:0.658909:0.470966:0.000000
 + :@0.663863:0.486936:0.683398:0.486936:0.683398:0.470438:0.663863:0.470438:0.000000:0.000000:0.000000
bx + c = 0:@0.683841:0.487051:0.755951:0.487051:0.755951:0.470583:0.683841:0.470583:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
, donde :@0.755951:0.486936:0.814325:0.486936:0.814325:0.470438:0.755951:0.470438:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a, b, c :@0.814768:0.487051:0.858481:0.487051:0.858481:0.470583:0.814768:0.470583:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.858924:0.486719:0.874972:0.486719:0.874972:0.472072:0.858924:0.472072:0.000000
R:@0.874972:0.485967:0.888881:0.485967:0.888881:0.472520:0.874972:0.472520:0.000000
,  :@0.888881:0.487051:0.895913:0.487051:0.895913:0.470583:0.888881:0.470583:0.000000:0.000000:0.000000
a  0,:@0.427690:0.504402:0.468456:0.504402:0.468456:0.487933:0.427690:0.487933:0.000000:0.000000:0.000000:0.000000:0.000000
≠   significa hallar, si existe, al menos, un elemento :@0.441696:0.504286:0.811972:0.504286:0.811972:0.487789:0.441696:0.487789:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.816300:0.503311:0.823276:0.503311:0.823276:0.487940:0.816300:0.487940:0.000000
∈:@0.827340:0.503797:0.840161:0.503797:0.840161:0.488602:0.827340:0.488602:0.000000
 que :@0.859737:0.504286:0.895916:0.504286:0.895916:0.487789:0.859737:0.487789:0.000000:0.000000:0.000000:0.000000:0.000000
satisface la ecuación. Si existe :@0.427695:0.523517:0.636528:0.523517:0.636528:0.507019:0.427695:0.507019:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.639795:0.522548:0.646772:0.522548:0.646772:0.507177:0.639795:0.507177:0.000000
∈:@0.650838:0.523034:0.663658:0.523034:0.663658:0.507838:0.650838:0.507838:0.000000
, tal que  ˆ:@0.681445:0.523523:0.760742:0.522338:0.760742:0.505840:0.681445:0.507025:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ax:@0.744077:0.523639:0.760337:0.523639:0.760337:0.507170:0.744077:0.507170:0.000000:0.000000
bx c:@0.784592:0.523639:0.825602:0.523639:0.825602:0.507170:0.784592:0.507170:0.000000:0.000000:0.000000:0.000000
x:@0.862437:0.523639:0.869912:0.523639:0.869912:0.507170:0.862437:0.507170:0.000000
+:@0.771300:0.524159:0.748470:0.524159:0.748470:0.507879:0.771300:0.507879:0.000000
+:@0.804706:0.524159:0.781876:0.524159:0.781876:0.507879:0.804706:0.507879:0.000000
ˆ:@0.793975:0.522338:0.801681:0.522338:0.801681:0.505840:0.793975:0.505840:0.000000
=0, ˆ  es :@0.828845:0.523523:0.895920:0.523523:0.895920:0.507025:0.828845:0.507025:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.761563:0.515487:0.766481:0.515487:0.766481:0.505939:0.761563:0.505939:0.000000
una raíz de la ecuación de segundo grado y diremos que la ecua-:@0.427697:0.540874:0.891849:0.540874:0.891849:0.524376:0.427697:0.524376:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ción de segundo grado tiene solución en  . Si no existe un núme-:@0.427697:0.558225:0.891757:0.558225:0.891757:0.541727:0.427697:0.541727:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.718755:0.557256:0.732664:0.557256:0.732664:0.543809:0.718755:0.543809:0.000000
ro real que satisfaga la ecuación de segundo grado, se dirá que esta :@0.427697:0.575575:0.895978:0.575575:0.895978:0.559078:0.427697:0.559078:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
no tiene solución en  .:@0.427697:0.592926:0.593704:0.592926:0.593704:0.576428:0.427697:0.576428:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.577039:0.591957:0.590949:0.591957:0.590949:0.578511:0.577039:0.578511:0.000000
Definición:@0.404251:0.617868:0.484335:0.617868:0.484335:0.600922:0.404251:0.600922:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i):@0.404251:0.642101:0.414404:0.642101:0.414404:0.625387:0.404251:0.625387:0.000000:0.000000
   Se dice que :@0.414019:0.641884:0.515566:0.641884:0.515566:0.625387:0.414019:0.625387:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
r :@0.518668:0.642000:0.528454:0.642000:0.528454:0.625531:0.518668:0.625531:0.000000:0.000000
 :@0.531537:0.641667:0.552016:0.641667:0.552016:0.627020:0.531537:0.627020:0.000000:0.000000
R:@0.555676:0.640915:0.569586:0.640915:0.569586:0.627469:0.555676:0.627469:0.000000
 es una raíz simple de   si para todo :@0.569200:0.641884:0.838644:0.641884:0.838644:0.625387:0.569200:0.625387:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.736348:0.642000:0.740644:0.642000:0.740644:0.625531:0.736348:0.625531:0.000000
x:@0.845580:0.640908:0.852556:0.640908:0.852556:0.625537:0.845580:0.625537:0.000000
∈:@0.856623:0.641394:0.869443:0.641394:0.869443:0.626198:0.856623:0.626198:0.000000
, :@0.889019:0.641884:0.895916:0.641884:0.895916:0.625387:0.889019:0.625387:0.000000:0.000000
 :@0.891774:0.641884:0.895916:0.641884:0.895916:0.625387:0.891774:0.625387:0.000000
fx:@0.433818:0.660608:0.455106:0.660608:0.455106:0.644139:0.433818:0.644139:0.000000:0.000000
xr Qx:@0.484293:0.660608:0.549505:0.660608:0.549505:0.644139:0.484293:0.644139:0.000000:0.000000:0.000000:0.000000:0.000000
−:@0.495177:0.661128:0.505754:0.661128:0.505754:0.644848:0.495177:0.644848:0.000000
()=(:@0.440946:0.660492:0.483560:0.660492:0.483560:0.643995:0.440946:0.643995:0.000000:0.000000:0.000000:0.000000
)( ),  donde   es un polinomio de grado 1 y  ( ) ≠ 0.:@0.515599:0.660492:0.889413:0.659235:0.889413:0.642737:0.515599:0.643995:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Q:@0.615480:0.659351:0.627367:0.659351:0.627367:0.642882:0.615480:0.642882:0.000000
Q r:@0.832330:0.659351:0.855429:0.659351:0.855429:0.642882:0.832330:0.642882:0.000000:0.000000:0.000000
ii):@0.404237:0.683931:0.419032:0.683931:0.419032:0.667216:0.404237:0.667216:0.000000:0.000000:0.000000
   Se dice que :@0.419032:0.683714:0.513933:0.683714:0.513933:0.667216:0.419032:0.667216:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
r :@0.514087:0.683830:0.523874:0.683830:0.523874:0.667361:0.514087:0.667361:0.000000:0.000000
 :@0.524047:0.683497:0.544526:0.683497:0.544526:0.668850:0.524047:0.668850:0.000000:0.000000
R:@0.544796:0.682745:0.558705:0.682745:0.558705:0.669298:0.544796:0.669298:0.000000
 es una raíz doble o de multiplicidad 2 si existe :@0.558320:0.683714:0.895936:0.683714:0.895936:0.667216:0.558320:0.667216:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
una constante  :@0.427682:0.702944:0.537514:0.702944:0.537514:0.686447:0.427682:0.686447:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.537128:0.703494:0.549285:0.703494:0.549285:0.684654:0.537128:0.684654:0.000000
 :@0.548899:0.703060:0.553041:0.703060:0.553041:0.686591:0.548899:0.686591:0.000000
 :@0.552656:0.702728:0.573135:0.702728:0.573135:0.688081:0.552656:0.688081:0.000000:0.000000
R:@0.573135:0.701976:0.587045:0.701976:0.587045:0.688529:0.573135:0.688529:0.000000
,  ≠ 0, tal que :@0.586274:0.702944:0.692327:0.702944:0.692327:0.686447:0.586274:0.686447:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.593171:0.703494:0.605327:0.703494:0.605327:0.684654:0.593171:0.684654:0.000000
 :@0.604942:0.703060:0.609084:0.703060:0.609084:0.686591:0.604942:0.686591:0.000000
() =(:@0.705116:0.702247:0.758951:0.702247:0.758951:0.686329:0.705116:0.686329:0.000000:0.000000:0.000000:0.000000:0.000000
),:@0.788322:0.702247:0.804978:0.702247:0.804978:0.686329:0.788322:0.686329:0.000000:0.000000
.:@0.870263:0.702247:0.872922:0.702247:0.872922:0.686329:0.870263:0.686329:0.000000
2:@0.794374:0.694494:0.799119:0.694494:0.799119:0.685280:0.794374:0.685280:0.000000
fx:@0.698246:0.702359:0.718787:0.702359:0.718787:0.686468:0.698246:0.686468:0.000000:0.000000
xr:@0.759665:0.702359:0.787660:0.702359:0.787660:0.686468:0.759665:0.686468:0.000000:0.000000
x:@0.827702:0.702359:0.834914:0.702359:0.834914:0.686468:0.827702:0.686468:0.000000
α:@0.738899:0.702861:0.750629:0.702861:0.755234:0.687152:0.743504:0.687152:0.000000
−:@0.769572:0.702861:0.779778:0.702861:0.779778:0.687152:0.769572:0.687152:0.000000
∀ ∈:@0.814577:0.702861:0.852388:0.702861:0.852388:0.687152:0.814577:0.687152:0.000000:0.000000:0.000000
Ejercicio resuelto:@0.404238:0.727806:0.522216:0.727806:0.522216:0.711019:0.404238:0.711019:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.:@0.404238:0.754005:0.416510:0.754005:0.416510:0.737291:0.404238:0.737291:0.000000:0.000000
   Sea  ()=2:@0.416510:0.753788:0.512252:0.753794:0.512252:0.737296:0.416510:0.737291:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.527857:0.754430:0.538434:0.754430:0.538434:0.738149:0.527857:0.738149:0.000000
+:@0.564827:0.754430:0.575404:0.754430:0.575404:0.738149:0.564827:0.738149:0.000000
∀∈:@0.607326:0.754430:0.644354:0.754430:0.644354:0.738149:0.607326:0.738149:0.000000:0.000000
16:@0.539570:0.753794:0.556485:0.753794:0.556485:0.737296:0.539570:0.737296:0.000000:0.000000
32,:@0.577311:0.753794:0.598406:0.753794:0.598406:0.737296:0.577311:0.737296:0.000000:0.000000:0.000000
. Entonces   = –4 es una raíz de :@0.662713:0.753794:0.895883:0.753794:0.895883:0.737297:0.662713:0.737296:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.519218:0.745758:0.524135:0.745758:0.524135:0.736210:0.519218:0.736210:0.000000
ft:@0.463045:0.753910:0.481386:0.753910:0.481386:0.737441:0.463045:0.737441:0.000000:0.000000
t:@0.512519:0.753910:0.518183:0.753910:0.518183:0.737441:0.512519:0.737441:0.000000
t:@0.556752:0.753910:0.562416:0.753910:0.562416:0.737441:0.556752:0.737441:0.000000
t:@0.620944:0.753910:0.626607:0.753910:0.626607:0.737441:0.620944:0.737441:0.000000
r:@0.741761:0.753910:0.747791:0.753910:0.747791:0.737441:0.741761:0.737441:0.000000
f:@0.427701:0.771261:0.431997:0.771261:0.431997:0.754792:0.427701:0.754792:0.000000
, pues  (–4) = 0, luego, :@0.431997:0.771145:0.596231:0.771145:0.596231:0.754647:0.431997:0.754647:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.478253:0.771261:0.482549:0.771261:0.482549:0.754792:0.478253:0.754792:0.000000
() =(:@0.609880:0.770755:0.648854:0.770755:0.648854:0.754624:0.609880:0.754624:0.000000:0.000000:0.000000:0.000000:0.000000
(–4))( )=(:@0.668577:0.770755:0.755133:0.770755:0.755133:0.754624:0.668577:0.754624:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4)( ),:@0.774855:0.770755:0.820648:0.770755:0.820648:0.754624:0.774855:0.754624:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
,:@0.885561:0.770755:0.888254:0.770755:0.888254:0.754624:0.885561:0.754624:0.000000
ft:@0.602911:0.770868:0.620843:0.770868:0.620843:0.754765:0.602911:0.754765:0.000000:0.000000
t:@0.648458:0.770868:0.653997:0.770868:0.653997:0.754765:0.648458:0.754765:0.000000
Q t:@0.703632:0.770868:0.727085:0.770868:0.727085:0.754765:0.703632:0.754765:0.000000:0.000000:0.000000
t:@0.754718:0.770868:0.760256:0.770868:0.760256:0.754765:0.754718:0.754765:0.000000
Qt:@0.788757:0.770868:0.812209:0.770868:0.812209:0.754765:0.788757:0.754765:0.000000:0.000000
t:@0.843686:0.770868:0.849224:0.770868:0.849224:0.754765:0.843686:0.754765:0.000000
−:@0.656540:0.771377:0.666881:0.771377:0.666881:0.755458:0.656540:0.755458:0.000000
+:@0.762404:0.771377:0.772746:0.771377:0.772746:0.755458:0.762404:0.755458:0.000000
∀∈:@0.830368:0.771377:0.866724:0.771377:0.866724:0.755458:0.830368:0.755458:0.000000:0.000000
:@0.870427:0.773766:0.884027:0.773766:0.884027:0.752899:0.870427:0.752899:0.000000
donde  ( ) =   + :@0.427691:0.788496:0.566652:0.788496:0.566652:0.771998:0.427691:0.771998:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Q t:@0.480170:0.788611:0.503673:0.788611:0.503673:0.772142:0.480170:0.772142:0.000000:0.000000:0.000000
at:@0.531608:0.788611:0.546134:0.788611:0.546134:0.772142:0.531608:0.772142:0.000000:0.000000
b,   t:@0.568096:0.788611:0.610364:0.788611:0.610364:0.772142:0.568096:0.772142:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∀:@0.590964:0.789045:0.604700:0.789045:0.604700:0.770205:0.590964:0.770205:0.000000
:@0.610364:0.788279:0.626412:0.788279:0.626412:0.773632:0.610364:0.773632:0.000000
R   :@0.626412:0.787527:0.666079:0.787527:0.666079:0.774080:0.626412:0.774080:0.000000:0.000000:0.000000:0.000000
, ,:@0.640322:0.788496:0.661263:0.788496:0.661263:0.771998:0.640322:0.771998:0.000000:0.000000:0.000000
a b:@0.649531:0.788611:0.677022:0.788611:0.677022:0.772142:0.649531:0.772142:0.000000:0.000000:0.000000
:@0.677022:0.788279:0.693070:0.788279:0.693070:0.773632:0.677022:0.773632:0.000000
R :@0.693070:0.787527:0.711796:0.787527:0.711796:0.774080:0.693070:0.774080:0.000000:0.000000
con   ≠ 0. Estudiemos si :@0.713472:0.788496:0.895951:0.788496:0.895951:0.771998:0.713472:0.771998:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.746011:0.788611:0.754989:0.788611:0.754989:0.772142:0.746011:0.772142:0.000000
 :@0.891791:0.788496:0.895933:0.788496:0.895933:0.771998:0.891791:0.771998:0.000000
r:@0.427710:0.805962:0.433741:0.805962:0.433741:0.789493:0.427710:0.789493:0.000000
 = –4  es una raíz doble. Puesto que :@0.433741:0.805846:0.689618:0.805846:0.689618:0.789349:0.433741:0.789349:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ft:@0.431789:0.825199:0.450129:0.825199:0.450129:0.808730:0.431789:0.808730:0.000000:0.000000
t:@0.477968:0.825199:0.483632:0.825199:0.483632:0.808730:0.477968:0.808730:0.000000
atb:@0.520486:0.825199:0.560731:0.825199:0.560731:0.808730:0.520486:0.808730:0.000000:0.000000:0.000000
at:@0.582674:0.825199:0.597123:0.825199:0.597123:0.808730:0.582674:0.808730:0.000000:0.000000
b:@0.626753:0.825199:0.636020:0.825199:0.636020:0.808730:0.626753:0.808730:0.000000
a t:@0.661354:0.825199:0.681255:0.825199:0.681255:0.808730:0.661354:0.808730:0.000000:0.000000:0.000000
b:@0.706955:0.825199:0.716221:0.825199:0.716221:0.808730:0.706955:0.808730:0.000000
t:@0.740976:0.825199:0.746640:0.825199:0.746640:0.808730:0.740976:0.808730:0.000000
t:@0.787097:0.825199:0.792761:0.825199:0.792761:0.808730:0.787097:0.808730:0.000000
+:@0.486862:0.825719:0.446136:0.825719:0.446136:0.809438:0.486862:0.809438:0.000000
+:@0.538166:0.825719:0.497439:0.825719:0.497439:0.809438:0.538166:0.809438:0.000000
+:@0.607906:0.825719:0.587909:0.825719:0.587909:0.809438:0.607906:0.809438:0.000000
+:@0.638480:0.825719:0.618483:0.825719:0.618483:0.809438:0.638480:0.809438:0.000000
+:@0.684505:0.825719:0.622162:0.825719:0.622162:0.809438:0.684505:0.809438:0.000000
+:@0.757424:0.825719:0.695081:0.825719:0.695081:0.809438:0.757424:0.809438:0.000000
+:@0.796012:0.825719:0.806589:0.825719:0.806589:0.809438:0.796012:0.809438:0.000000
()=(:@0.438930:0.825083:0.478405:0.825083:0.478405:0.808585:0.438930:0.808585:0.000000:0.000000:0.000000:0.000000
4)(:@0.500598:0.825083:0.520480:0.825083:0.520480:0.808585:0.500598:0.808585:0.000000:0.000000:0.000000
)=:@0.560224:0.825083:0.579836:0.825083:0.579836:0.808585:0.560224:0.808585:0.000000:0.000000
(:@0.621218:0.825083:0.627171:0.825083:0.627171:0.808585:0.621218:0.808585:0.000000
4):@0.652216:0.825083:0.675662:0.825083:0.675662:0.808585:0.652216:0.808585:0.000000:0.000000
4=2:@0.698241:0.825083:0.740759:0.825083:0.740759:0.808585:0.698241:0.808585:0.000000:0.000000:0.000000
16:@0.769965:0.825083:0.786880:0.825083:0.786880:0.808585:0.769965:0.808585:0.000000:0.000000
32, y, por la :@0.809324:0.825083:0.895915:0.825083:0.895915:0.808585:0.809324:0.808585:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.598162:0.817047:0.603079:0.817047:0.603079:0.807499:0.598162:0.807499:0.000000
2:@0.747682:0.817047:0.752600:0.817047:0.752600:0.807499:0.747682:0.807499:0.000000
igualdad de polinomios, tenemos   = 2,   + 4  = 16,  4  = 32, con lo :@0.427692:0.842434:0.896048:0.842434:0.896048:0.825936:0.427692:0.825936:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.664479:0.842549:0.673457:0.842549:0.673457:0.826081:0.664479:0.826081:0.000000
b:@0.704647:0.842549:0.713914:0.842549:0.713914:0.826081:0.704647:0.826081:0.000000
a:@0.739306:0.842549:0.748283:0.842549:0.748283:0.826081:0.739306:0.826081:0.000000
b:@0.799509:0.842549:0.808776:0.842549:0.808776:0.826081:0.799509:0.826081:0.000000
cual   = 2 y   = 8. Luego, :@0.427692:0.860406:0.606973:0.860406:0.606973:0.843909:0.427692:0.843909:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.460713:0.860522:0.469690:0.860522:0.469690:0.844053:0.460713:0.844053:0.000000
b:@0.513230:0.860522:0.522496:0.860522:0.522496:0.844053:0.513230:0.844053:0.000000
+:@0.668031:0.862186:0.678546:0.862186:0.678546:0.846000:0.668031:0.846000:0.000000
+:@0.718153:0.862186:0.728668:0.862186:0.728668:0.846000:0.718153:0.846000:0.000000
+:@0.784612:0.862186:0.795127:0.862186:0.795127:0.846000:0.784612:0.846000:0.000000
∀ ∈:@0.833796:0.862186:0.870358:0.862186:0.870358:0.846000:0.833796:0.846000:0.000000:0.000000:0.000000
ft:@0.613083:0.861668:0.631316:0.861668:0.631316:0.845296:0.613083:0.845296:0.000000:0.000000
t:@0.659393:0.861668:0.665024:0.861668:0.665024:0.845296:0.659393:0.845296:0.000000
t:@0.709515:0.861668:0.715146:0.861668:0.715146:0.845296:0.709515:0.845296:0.000000
t:@0.775972:0.861668:0.781603:0.861668:0.781603:0.845296:0.775972:0.845296:0.000000
t:@0.847334:0.861668:0.852965:0.861668:0.852965:0.845296:0.847334:0.845296:0.000000
() =(:@0.620149:0.861553:0.659776:0.861553:0.659776:0.845152:0.620149:0.845152:0.000000:0.000000:0.000000:0.000000:0.000000
4)(2:@0.681457:0.861553:0.709266:0.861553:0.709266:0.845152:0.681457:0.845152:0.000000:0.000000:0.000000:0.000000
8) =2(:@0.731157:0.861553:0.776357:0.861553:0.776357:0.845152:0.731157:0.845152:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4),:@0.798019:0.861553:0.823453:0.861553:0.823453:0.845152:0.798019:0.845152:0.000000:0.000000:0.000000
.:@0.885144:0.861553:0.887882:0.861553:0.887882:0.845152:0.885144:0.845152:0.000000
2:@0.812561:0.853565:0.817449:0.853565:0.817449:0.844072:0.812561:0.844072:0.000000
 :@0.891773:0.860413:0.895915:0.860413:0.895915:0.843916:0.891773:0.843916:0.000000
Es decir que   = –4 es una raíz doble o de multiplicidad 2. La escri-:@0.427692:0.877764:0.891782:0.877764:0.891782:0.861266:0.427692:0.861266:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
r:@0.516522:0.877880:0.522552:0.877880:0.522552:0.861411:0.516522:0.861411:0.000000
tura de la función  , en la forma  ()=2(:@0.427692:0.895736:0.712383:0.897001:0.712383:0.880503:0.427692:0.879239:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.556634:0.895852:0.560931:0.895852:0.560931:0.879383:0.556634:0.879383:0.000000
+:@0.720051:0.897637:0.730627:0.897637:0.730627:0.881356:0.720051:0.881356:0.000000
∀ ∈:@0.767328:0.897637:0.804355:0.897637:0.804355:0.881356:0.767328:0.881356:0.000000:0.000000:0.000000
4),:@0.732978:0.897001:0.758408:0.897001:0.758408:0.880503:0.732978:0.880503:0.000000:0.000000:0.000000
, se cono-:@0.823447:0.897001:0.891768:0.895743:0.891768:0.879246:0.823447:0.880503:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.747587:0.888965:0.752504:0.888965:0.752504:0.879416:0.747587:0.879416:0.000000
ft:@0.656966:0.897116:0.675307:0.897116:0.675307:0.880648:0.656966:0.880648:0.000000:0.000000
t:@0.711988:0.897116:0.717652:0.897116:0.717652:0.880648:0.711988:0.880648:0.000000
t:@0.780938:0.897116:0.786602:0.897116:0.786602:0.880648:0.780938:0.880648:0.000000
ce como factorización del polinomio  .:@0.427687:0.913094:0.701173:0.913094:0.701173:0.896596:0.427687:0.896596:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.694122:0.913210:0.698418:0.913210:0.698418:0.896741:0.694122:0.896741:0.000000
Saberes previos:@0.199646:0.093079:0.307805:0.093079:0.307805:0.077606:0.199646:0.077606:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Qué es una ecuación :@0.199884:0.121706:0.345441:0.121706:0.345441:0.106643:0.199884:0.106643:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuadrática en el conjunto  ?:@0.153341:0.137548:0.340446:0.137548:0.340446:0.122485:0.153341:0.122485:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.322539:0.136664:0.335239:0.136664:0.335239:0.124386:0.322539:0.124386:0.000000
Desequilibrio cognitivo:@0.199644:0.181136:0.363492:0.181136:0.363492:0.165664:0.199644:0.165664:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si   es una expresión :@0.199880:0.209764:0.337045:0.209764:0.337045:0.194701:0.199880:0.194701:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.214445:0.209869:0.221551:0.209869:0.221551:0.194833:0.214445:0.194833:0.000000
algebraica en   y   es un real :@0.153337:0.225606:0.344908:0.225606:0.344908:0.210543:0.153337:0.210543:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.241338:0.224721:0.254038:0.224721:0.254038:0.212444:0.241338:0.212444:0.000000
k:@0.268743:0.225711:0.276272:0.225711:0.276272:0.210675:0.268743:0.210675:0.000000
negativo, entonces, ¿qué tipo :@0.153337:0.241448:0.345309:0.241448:0.345309:0.226385:0.153337:0.226385:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de solución tendrá la ecuación :@0.153337:0.257290:0.355971:0.257290:0.355971:0.242227:0.153337:0.242227:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.153337:0.273237:0.160444:0.273237:0.160444:0.258201:0.153337:0.258201:0.000000
2:@0.160450:0.267331:0.164973:0.267331:0.164973:0.258549:0.160450:0.258549:0.000000
 = – ?:@0.164972:0.273132:0.204725:0.273132:0.204725:0.258069:0.164972:0.258069:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
k:@0.191990:0.273237:0.199519:0.273237:0.199519:0.258201:0.191990:0.258201:0.000000
Competencia :@0.199644:0.619888:0.297267:0.619888:0.297267:0.604415:0.199644:0.604415:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
comunicacional:@0.199644:0.632456:0.311603:0.632456:0.311603:0.616983:0.199644:0.616983:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Aprende la siguiente :@0.193071:0.656929:0.329536:0.656929:0.329536:0.641866:0.193071:0.641866:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
simbología matemática::@0.153335:0.672771:0.308107:0.672771:0.308107:0.657708:0.153335:0.657708:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i):@0.153335:0.695940:0.162956:0.695940:0.162956:0.680679:0.153335:0.680679:0.000000:0.000000
 Un número real   se dice una :@0.162956:0.695742:0.358434:0.695742:0.358434:0.680679:0.162956:0.680679:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
r:@0.273088:0.695848:0.278593:0.695848:0.278593:0.680811:0.273088:0.680811:0.000000
raíz de la función   si satisface la :@0.153335:0.711584:0.360262:0.711584:0.360262:0.696521:0.153335:0.696521:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.267828:0.711690:0.271751:0.711690:0.271751:0.696653:0.267828:0.696653:0.000000
condición  ( )=0. :@0.153335:0.727426:0.266562:0.727426:0.266562:0.712363:0.153335:0.712363:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f r:@0.222340:0.727532:0.237204:0.727532:0.237204:0.712495:0.222340:0.712495:0.000000:0.000000:0.000000
ii):@0.153335:0.750595:0.166844:0.750595:0.166844:0.735334:0.153335:0.735334:0.000000:0.000000:0.000000
 Se dice que la función   no :@0.166844:0.750397:0.345787:0.750397:0.345787:0.735334:0.166844:0.735334:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.316764:0.750502:0.320686:0.750502:0.320686:0.735466:0.316764:0.735466:0.000000
tiene raíces en   si  ( )≠0 para :@0.153335:0.766239:0.354070:0.766239:0.354070:0.751176:0.153335:0.751176:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.249304:0.765354:0.262004:0.765354:0.262004:0.753077:0.249304:0.753077:0.000000
f x:@0.278750:0.766344:0.294933:0.766344:0.294933:0.751308:0.278750:0.751308:0.000000:0.000000:0.000000
todo ×:@0.153335:0.782081:0.199051:0.782081:0.199051:0.767018:0.153335:0.767018:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.199051:0.781883:0.213704:0.781883:0.213704:0.768510:0.199051:0.768510:0.000000
R:@0.213704:0.781196:0.226404:0.781196:0.226404:0.768919:0.213704:0.768919:0.000000
. :@0.226404:0.782081:0.232701:0.782081:0.232701:0.767018:0.226404:0.767018:0.000000:0.000000