85:@0.921900:0.510692:0.940807:0.510692:0.940807:0.494068:0.921900:0.494068:0.000000:0.000000
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 :@0.260784:0.113160:0.881629:0.113160:0.881629:0.102730:0.260784:0.102730:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de la ecuación de segundo grado; juzga la validez de las soluciones obtenidas en el contexto del problema. :@0.260784:0.123721:0.763182:0.123721:0.763182:0.113292:0.260784:0.113292:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f) :@0.547679:0.590774:0.564503:0.590774:0.564503:0.573874:0.547679:0.573874:0.000000:0.000000:0.000000
José creó un cuadrado algo especial: su :@0.580922:0.590774:0.888700:0.590774:0.888700:0.574385:0.580922:0.574385:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
área más su perímetro suman 1 440.:@0.580922:0.607371:0.845484:0.607371:0.845484:0.590982:0.580922:0.590982:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.547679:0.627535:0.551714:0.627535:0.551714:0.611146:0.547679:0.611146:0.000000
¿Cuánto mide cada lado del cuadrado?:@0.580922:0.627535:0.866808:0.627535:0.866808:0.611146:0.580922:0.611146:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g) :@0.547679:0.770207:0.567599:0.770207:0.567599:0.753307:0.547679:0.753307:0.000000:0.000000:0.000000
La suma de los cuadrados de dos núme-:@0.580922:0.770207:0.884646:0.770207:0.884646:0.753819:0.580922:0.753819:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ros pares consecutivos es 340. ¿Cuáles :@0.580922:0.786804:0.888717:0.786804:0.888717:0.770415:0.580922:0.770415:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
son esos números?:@0.580922:0.803400:0.720657:0.803400:0.720657:0.787011:0.580922:0.787011:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.514435:0.917279:0.518158:0.917279:0.518158:0.900143:0.514435:0.900143:0.000000
  :@0.547679:0.917279:0.555123:0.917279:0.555123:0.900143:0.547679:0.900143:0.000000:0.000000
e) :@0.547679:0.172018:0.566548:0.172018:0.566548:0.155117:0.547679:0.155117:0.000000:0.000000:0.000000
Karla visitó la feria del libro. Allí compró :@0.580922:0.172018:0.888700:0.172018:0.888700:0.155629:0.580922:0.155629:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
una colección de libros por $ 90. Si hubie-:@0.580922:0.188614:0.884646:0.188614:0.884646:0.172225:0.580922:0.172225:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ra comprado 3 libros más por la misma :@0.580922:0.205210:0.888684:0.205210:0.888684:0.188821:0.580922:0.188821:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cantidad de dinero, cada libro le hubiese :@0.580922:0.221807:0.888682:0.221807:0.888682:0.205418:0.580922:0.205418:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
costado $ 1 menos.:@0.580922:0.238403:0.723384:0.238403:0.723384:0.222014:0.580922:0.222014:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i) :@0.580038:0.268664:0.594116:0.268664:0.594116:0.251763:0.580038:0.251763:0.000000:0.000000:0.000000
¿Cuántos libros compró Karla?:@0.613281:0.268664:0.834118:0.268664:0.834118:0.252275:0.613281:0.252275:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
        :@0.580038:0.391505:0.608847:0.391505:0.608847:0.374369:0.580038:0.374369:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ii) :@0.580036:0.420303:0.598832:0.420303:0.598832:0.403403:0.580036:0.403403:0.000000:0.000000:0.000000:0.000000
¿Cuánto pagó por cada libro de la  :@0.613279:0.420303:0.869331:0.420303:0.869331:0.403914:0.613279:0.403914:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
colección?:@0.613279:0.436900:0.691136:0.436900:0.691136:0.420511:0.613279:0.420511:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
        :@0.580036:0.557901:0.608846:0.557901:0.608846:0.540765:0.580036:0.540765:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R.:@0.615826:0.530226:0.630660:0.530226:0.630660:0.513326:0.615826:0.513326:0.000000:0.000000
1. :@0.120583:0.172021:0.139324:0.172021:0.139324:0.154886:0.120583:0.154886:0.000000:0.000000:0.000000
Resuelve:@0.153826:0.172021:0.221988:0.172021:0.221988:0.155397:0.153826:0.155397:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 los siguientes problemas. :@0.221988:0.172021:0.414869:0.172021:0.414869:0.155632:0.221988:0.155632:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a) :@0.153826:0.205850:0.172549:0.205850:0.172549:0.188950:0.153826:0.188950:0.000000:0.000000:0.000000
Una piscina rectangular fue construida :@0.187070:0.205850:0.487403:0.205850:0.487403:0.189461:0.187070:0.189461:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
con un área de 1 000 m2 y un perímetro :@0.187070:0.222447:0.495880:0.222447:0.495880:0.206058:0.187070:0.206058:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de 140 m. ¿Qué longitud  :@0.187070:0.239043:0.376449:0.239043:0.376449:0.222654:0.187070:0.222654:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tiene cada lado de la piscina?:@0.187070:0.255639:0.401088:0.255639:0.401088:0.239251:0.187070:0.239251:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b) :@0.153820:0.398309:0.173851:0.398309:0.173851:0.381409:0.153820:0.381409:0.000000:0.000000:0.000000
¿Cuáles son los dos números positivos,  :@0.187063:0.398309:0.497901:0.398309:0.497901:0.381920:0.187063:0.381920:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tales que, la suma de sus cuadrados sea :@0.187063:0.414906:0.497864:0.414906:0.497864:0.398517:0.187063:0.398517:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
193 y su diferencia sea 5?:@0.187063:0.431502:0.373328:0.431502:0.373328:0.415113:0.187063:0.415113:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.120576:0.545381:0.124299:0.545381:0.124299:0.528245:0.120576:0.528245:0.000000
  :@0.153820:0.545381:0.161264:0.545381:0.161264:0.528245:0.153820:0.528245:0.000000:0.000000
c) :@0.153820:0.574178:0.171455:0.574178:0.171455:0.557277:0.153820:0.557277:0.000000:0.000000:0.000000
La suma de los cuadrados de dos números  :@0.187063:0.574178:0.497901:0.574178:0.497901:0.557789:0.187063:0.557789:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
enteros, negativos y consecutivos es 481.:@0.187063:0.590774:0.487356:0.590774:0.487356:0.574385:0.187063:0.574385:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.153820:0.610939:0.157855:0.610939:0.157855:0.594550:0.153820:0.594550:0.000000
¿Cuáles son esos números?:@0.187063:0.610939:0.388311:0.610939:0.388311:0.594550:0.187063:0.594550:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.120576:0.724818:0.124299:0.724818:0.124299:0.707682:0.120576:0.707682:0.000000
  :@0.153820:0.724818:0.161264:0.724818:0.161264:0.707682:0.153820:0.707682:0.000000:0.000000
d) :@0.153820:0.753611:0.173887:0.753611:0.173887:0.736710:0.153820:0.736710:0.000000:0.000000:0.000000
Beatriz es dos años mayor que Ricardo y :@0.187063:0.753611:0.497917:0.753611:0.497917:0.737222:0.187063:0.737222:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la suma de los cuadrados de ambas eda-:@0.187063:0.770207:0.493828:0.770207:0.493828:0.753819:0.187063:0.753819:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
des es 1 154. ¿Cuál es la edad de Beatriz  :@0.187063:0.786804:0.497901:0.786804:0.497901:0.770415:0.187063:0.770415:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y Ricardo?:@0.187063:0.803400:0.261234:0.803400:0.261234:0.787011:0.187063:0.787011:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.120576:0.917279:0.124299:0.917279:0.124299:0.900143:0.120576:0.900143:0.000000
  :@0.153820:0.917279:0.161264:0.917279:0.161264:0.900143:0.153820:0.900143:0.000000:0.000000
R.:@0.186229:0.325884:0.201063:0.325884:0.201063:0.308983:0.186229:0.308983:0.000000:0.000000
R.:@0.611760:0.367375:0.626594:0.367375:0.626594:0.350474:0.611760:0.350474:0.000000:0.000000
R.:@0.584303:0.676205:0.599137:0.676205:0.599137:0.659305:0.584303:0.659305:0.000000:0.000000
R.:@0.584303:0.850619:0.599137:0.850619:0.599137:0.833719:0.584303:0.833719:0.000000:0.000000
R.:@0.186247:0.525787:0.201082:0.525787:0.201082:0.508886:0.186247:0.508886:0.000000:0.000000
R.:@0.186247:0.682152:0.201082:0.682152:0.201082:0.665252:0.186247:0.665252:0.000000:0.000000
R.:@0.186247:0.892913:0.201082:0.892913:0.201082:0.876012:0.186247:0.876012:0.000000:0.000000
Shutterstock, (2021). 744562936:@0.900777:0.423365:0.900777:0.311768:0.886881:0.311768:0.886881:0.423365:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
www.freepik.es, (2021). :@0.505436:0.366914:0.505436:0.284792:0.491540:0.284792:0.491540:0.366914:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000