43:@0.942772:0.974518:0.963274:0.974518:0.963274:0.956333:0.942772:0.956333:0.000000:0.000000 Pensamiento variacional:@0.707231:0.043661:0.926913:0.043661:0.926913:0.024916:0.707231:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Dos o más ecuaciones son :@0.740294:0.183107:0.901088:0.183107:0.901088:0.169661:0.740294:0.169661:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 equivalentes si todas tienen la :@0.740294:0.196723:0.921852:0.196723:0.921852:0.183277:0.740294:0.183277:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 misma solución.:@0.740294:0.210339:0.836402:0.210339:0.836402:0.196893:0.740294:0.196893:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Competencia :@0.740294:0.145974:0.838985:0.145974:0.838985:0.130568:0.740294:0.130568:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática :@0.740294:0.161103:0.828908:0.161103:0.828908:0.145697:0.740294:0.145697:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 8.3 Solución de una ecuación:@0.073089:0.137383:0.301576:0.137383:0.301576:0.120436:0.073089:0.120436:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Es el valor que al ser reemplazado en la variable hace que la igualdad se cumpla.:@0.073089:0.160458:0.653584:0.160458:0.653584:0.144024:0.073089:0.144024:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Para lograr llegar a la solución de una ecuación debemos transformar la ecuación inicial :@0.073089:0.183534:0.710873:0.183534:0.710873:0.167100:0.073089:0.167100:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 mediante la aplicación de las propiedades de la igualdad, en otras ecuaciones :@0.073089:0.200176:0.710273:0.200176:0.710273:0.183742:0.073089:0.183742:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 equivalentes hasta lograr despejar la variable o incógnita.:@0.073089:0.216818:0.486838:0.216818:0.486838:0.200384:0.073089:0.200384:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Veamos un ejemplo en el que solucionamos una ecuación en el conjunto de los números :@0.073089:0.239895:0.710422:0.239895:0.710422:0.223461:0.073089:0.223461:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 naturales. Consideremos la ecuación que creamos inicialmente.:@0.073089:0.256536:0.532219:0.256536:0.532219:0.240103:0.073089:0.240103:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1. 6 4 32:@0.073089:0.279607:0.185745:0.279607:0.185745:0.263173:0.073089:0.263173:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.112200:0.279607:0.119655:0.279607:0.119655:0.263201:0.112200:0.263201:0.000000 2 5:@0.121801:0.279052:0.165718:0.279052:0.165718:0.265336:0.121801:0.265336:0.000000:0.000000:0.000000 Esta es la ecuación inicial:@0.314062:0.279607:0.494674:0.279607:0.494674:0.263173:0.314062:0.263173:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Empezamos con la aplicación de la propiedad aditiva de las igualdades con el fin de que :@0.073089:0.302681:0.709851:0.302681:0.709851:0.286247:0.073089:0.286247:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 el término 6x quede solo al lado izquierdo de la ecuación, para lo cual sumamos 4 a :@0.073089:0.319323:0.709871:0.319323:0.709871:0.302889:0.073089:0.302889:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ambos lados de la ecuación inicial.:@0.073089:0.335965:0.322978:0.335965:0.322978:0.319531:0.073089:0.319531:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2. 6 4 4 32 4 que se convierte en::@0.073089:0.363328:0.400172:0.363328:0.400172:0.346894:0.073089:0.346894:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.112200:0.363328:0.119655:0.363328:0.119655:0.346922:0.112200:0.346922:0.000000 2 1 5:@0.121801:0.362773:0.194303:0.362773:0.194303:0.349057:0.121801:0.349057:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.216455:0.362773:0.231788:0.362773:0.231788:0.349057:0.216455:0.349057:0.000000 3. 6 36:@0.073089:0.383544:0.157162:0.383544:0.157162:0.367110:0.073089:0.367110:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.112200:0.383544:0.119655:0.383544:0.119655:0.367138:0.112200:0.367138:0.000000 5:@0.121801:0.382989:0.137135:0.382989:0.137135:0.369273:0.121801:0.369273:0.000000 Ahora aplicamos la propiedad multiplicativa de las igualdad, para lo cual dividimos :@0.073089:0.406618:0.710655:0.406618:0.710655:0.390184:0.073089:0.390184:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ambos lados de la igualdad entre 6, con el fin de despejar la variable y de esta forma, :@0.073089:0.423260:0.710400:0.423260:0.710400:0.406826:0.073089:0.406826:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.578386:0.423260:0.585841:0.423260:0.585841:0.406854:0.578386:0.406854:0.000000 poder encontrar la solución.:@0.073089:0.439902:0.276599:0.439902:0.276599:0.423468:0.073089:0.423468:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 4.:@0.073089:0.470910:0.085201:0.470910:0.085201:0.454476:0.073089:0.454476:0.000000:0.000000 6:@0.109579:0.464102:0.118562:0.464102:0.118562:0.447668:0.109579:0.447668:0.000000 x:@0.118488:0.464102:0.125943:0.464102:0.125943:0.447696:0.118488:0.447696:0.000000 6:@0.113279:0.481645:0.122262:0.481645:0.122262:0.465211:0.113279:0.465211:0.000000 :@0.132145:0.470910:0.153638:0.470910:0.153638:0.454476:0.132145:0.454476:0.000000:0.000000:0.000000 5:@0.134365:0.470355:0.149699:0.470355:0.149699:0.456639:0.134365:0.456639:0.000000 36:@0.157351:0.463083:0.175243:0.463083:0.175243:0.446649:0.157351:0.446649:0.000000:0.000000 6:@0.161806:0.480626:0.170788:0.480626:0.170788:0.464192:0.161806:0.464192:0.000000 que se convierte en::@0.253813:0.470910:0.400164:0.470910:0.400164:0.454476:0.253813:0.454476:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5.:@0.073089:0.498273:0.085201:0.498273:0.085201:0.481839:0.073089:0.481839:0.000000:0.000000 x:@0.103290:0.498273:0.110745:0.498273:0.110745:0.481867:0.103290:0.481867:0.000000 6:@0.110679:0.498273:0.139350:0.498273:0.139350:0.481839:0.110679:0.481839:0.000000:0.000000:0.000000:0.000000 5:@0.112899:0.497718:0.128233:0.497718:0.128233:0.484003:0.112899:0.484003:0.000000 Las igualdades 1, 2, 3, 4 y 5 que se obtuvieron en el proceso, son equivalentes, lo que :@0.073089:0.522062:0.710155:0.522062:0.710155:0.505628:0.073089:0.505628:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 quiere decir que todas tienen la misma solución.:@0.073089:0.538704:0.424082:0.538704:0.424082:0.522270:0.073089:0.522270:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Por tanto la solución de la ecuación 6x 4 32 es: :@0.073089:0.561780:0.445454:0.561779:0.445454:0.545345:0.073089:0.545347:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 5:@0.354757:0.561226:0.398670:0.561224:0.398670:0.547509:0.354757:0.547510:0.000000:0.000000:0.000000 Ejemplo 1.:@0.073089:0.594635:0.152608:0.594635:0.152608:0.577966:0.073089:0.577966:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Encuentra la solución de la ecuación :@0.152498:0.594635:0.429030:0.594635:0.429030:0.578202:0.152498:0.578202:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.073089:0.611277:0.080544:0.611277:0.080544:0.594871:0.073089:0.594871:0.000000 10 15 y haz la correspondiente verificación.:@0.080478:0.611277:0.427051:0.611277:0.427051:0.594843:0.080478:0.594843:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.082698:0.610723:0.098031:0.610723:0.098031:0.597007:0.082698:0.597007:0.000000 5:@0.120184:0.610723:0.135517:0.610723:0.135517:0.597007:0.120184:0.597007:0.000000 Pasos:@0.138370:0.632348:0.178998:0.632348:0.178998:0.616942:0.138370:0.616942:0.000000:0.000000:0.000000:0.000000:0.000000 Justificación:@0.320183:0.632348:0.409040:0.632348:0.409040:0.616942:0.320183:0.616942:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.121201:0.648435:0.127978:0.648435:0.127978:0.633521:0.121201:0.633521:0.000000 10 15:@0.127924:0.648430:0.196167:0.648430:0.196167:0.633490:0.127924:0.633490:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.129942:0.647926:0.143882:0.647926:0.143882:0.635457:0.129942:0.635457:0.000000 5:@0.164021:0.647926:0.177960:0.647926:0.177960:0.635457:0.164021:0.635457:0.000000 x :@0.090469:0.664512:0.099857:0.664512:0.099857:0.649598:0.090469:0.649598:0.000000:0.000000 1:@0.098548:0.664008:0.112487:0.664008:0.112487:0.651539:0.098548:0.651539:0.000000 10 10 15 10:@0.112069:0.664512:0.226904:0.664512:0.226904:0.649572:0.112069:0.649572:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.130953:0.664008:0.144892:0.664008:0.144892:0.651539:0.130953:0.651539:0.000000 5:@0.163359:0.664008:0.177298:0.664008:0.177298:0.651539:0.163359:0.651539:0.000000 2:@0.195762:0.664008:0.209701:0.664008:0.209701:0.651539:0.195762:0.651539:0.000000 Propiedad aditiva de la igualdad:@0.258817:0.664512:0.470571:0.664512:0.470571:0.649572:0.258817:0.649572:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x 5:@0.142098:0.680594:0.175268:0.680594:0.175268:0.665654:0.142098:0.665654:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.151221:0.680090:0.165161:0.680090:0.165161:0.667621:0.151221:0.667621:0.000000 Solución::@0.073089:0.699710:0.142959:0.699710:0.142959:0.683040:0.073089:0.683040:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5 :@0.142849:0.699710:0.159747:0.699710:0.159747:0.683276:0.142849:0.683276:0.000000:0.000000:0.000000 Verificación: :@0.194261:0.699710:0.284696:0.699710:0.284696:0.683276:0.194261:0.683276:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5 10 15:@0.317129:0.699710:0.401087:0.699710:0.401087:0.683276:0.317129:0.683276:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.328241:0.699155:0.343574:0.699155:0.343574:0.685439:0.328241:0.685439:0.000000 5:@0.365726:0.699155:0.381059:0.699155:0.381059:0.685439:0.365726:0.685439:0.000000 15 15:@0.345701:0.719926:0.401087:0.719926:0.401087:0.703492:0.345701:0.703492:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.365726:0.719371:0.381059:0.719371:0.381059:0.705655:0.365726:0.705655:0.000000 Ejemplo 2.:@0.073089:0.740141:0.152608:0.740141:0.152608:0.723471:0.073089:0.723471:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Encuentra la solución de la ecuación :@0.152498:0.740141:0.429030:0.740141:0.429030:0.723707:0.152498:0.723707:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 12 5 41 y haz la correspondiente verificación.:@0.073089:0.756782:0.435953:0.756782:0.435953:0.740349:0.073089:0.740349:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.090889:0.756782:0.098344:0.756782:0.098344:0.740376:0.090889:0.740376:0.000000 1 5:@0.100502:0.756228:0.144419:0.756228:0.144419:0.742512:0.100502:0.742512:0.000000:0.000000:0.000000 Pasos:@0.127697:0.778747:0.168325:0.778747:0.168325:0.763341:0.127697:0.763341:0.000000:0.000000:0.000000:0.000000:0.000000 Justificación:@0.309511:0.778747:0.398367:0.778747:0.398367:0.763341:0.309511:0.763341:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 12 5 41:@0.106646:0.796612:0.189373:0.796616:0.189373:0.781676:0.106646:0.781672:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.122828:0.796612:0.129605:0.796612:0.129605:0.781697:0.122828:0.781697:0.000000 1 5:@0.131576:0.796111:0.171167:0.796111:0.171167:0.783643:0.131576:0.783643:0.000000:0.000000:0.000000 12 5 5 41 5:@0.081512:0.814484:0.214509:0.814484:0.214509:0.799544:0.081512:0.799544:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.097693:0.814484:0.104470:0.814484:0.104470:0.799570:0.097693:0.799570:0.000000 1 2 5:@0.106433:0.813980:0.172343:0.813980:0.172343:0.801511:0.106433:0.801511:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.190462:0.813980:0.204402:0.813980:0.204402:0.801511:0.190462:0.801511:0.000000 Propiedad aditiva de la igualdad:@0.248144:0.814484:0.459898:0.814484:0.459898:0.799544:0.248144:0.799544:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 12x 36:@0.119286:0.832353:0.176742:0.832353:0.176742:0.817413:0.119286:0.817413:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.144597:0.831848:0.158536:0.831848:0.158536:0.819380:0.144597:0.819380:0.000000 36:@0.111110:0.852637:0.129002:0.852637:0.129002:0.836203:0.111110:0.836203:0.000000:0.000000 x:@0.128910:0.852637:0.136364:0.852637:0.136364:0.836231:0.128910:0.836231:0.000000 12:@0.114791:0.870180:0.132683:0.870180:0.132683:0.853746:0.114791:0.853746:0.000000:0.000000 :@0.141297:0.859445:0.162790:0.859445:0.162790:0.843011:0.141297:0.843011:0.000000:0.000000:0.000000 5:@0.143517:0.858890:0.158850:0.858890:0.158850:0.845174:0.143517:0.845174:0.000000 36:@0.166504:0.852637:0.184396:0.852637:0.184396:0.836203:0.166504:0.836203:0.000000:0.000000 12:@0.166504:0.870180:0.184396:0.870180:0.184396:0.853746:0.166504:0.853746:0.000000:0.000000 Propiedad multiplicativa de la igualdad:@0.225426:0.860673:0.482662:0.860673:0.482662:0.845733:0.225426:0.845733:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x 3:@0.131425:0.888992:0.164595:0.888992:0.164595:0.874052:0.131425:0.874052:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.140550:0.888487:0.154490:0.888487:0.154490:0.876019:0.140550:0.876019:0.000000 Solución::@0.073089:0.909001:0.142959:0.909001:0.142959:0.892332:0.073089:0.892332:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3 :@0.142849:0.909001:0.159741:0.909001:0.159741:0.892568:0.142849:0.892568:0.000000:0.000000:0.000000 Verificación: 12 (3) 5 41:@0.194261:0.909001:0.401087:0.909001:0.401087:0.892568:0.194261:0.892568:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1 5:@0.337143:0.908447:0.381059:0.908447:0.381059:0.894731:0.337143:0.894731:0.000000:0.000000:0.000000 36 5 41:@0.317114:0.929217:0.401087:0.929217:0.401087:0.912783:0.317114:0.912783:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1 5:@0.337143:0.928662:0.381059:0.928662:0.381059:0.914946:0.337143:0.914946:0.000000:0.000000:0.000000 Ejemplo 3.:@0.514231:0.594635:0.596364:0.594635:0.596364:0.577966:0.514231:0.577966:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 El largo de un rectángulo es el doble de su :@0.596493:0.594635:0.930848:0.594635:0.930848:0.578202:0.596493:0.578202:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ancho y su perímetro es 48 m. Encuentra las dimensiones :@0.514231:0.611277:0.931196:0.611277:0.931196:0.594843:0.514231:0.594843:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 del rectángulo.:@0.514231:0.627919:0.622887:0.627919:0.622887:0.611485:0.514231:0.611485:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Solución::@0.514231:0.650996:0.584101:0.650996:0.584101:0.634326:0.514231:0.634326:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 P 48 m:@0.514231:0.674069:0.579924:0.674069:0.579924:0.657635:0.514231:0.657635:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.525610:0.673514:0.540943:0.673514:0.540943:0.659798:0.525610:0.659798:0.000000 x:@0.514231:0.701432:0.521686:0.701432:0.521686:0.685026:0.514231:0.685026:0.000000 ancho:@0.521619:0.701432:0.587105:0.701432:0.587105:0.684998:0.521619:0.684998:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.523839:0.700877:0.539173:0.700877:0.539173:0.687162:0.523839:0.687162:0.000000 2 largo:@0.514231:0.728795:0.587238:0.728795:0.587238:0.712361:0.514231:0.712361:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.523140:0.728795:0.530595:0.728795:0.530595:0.712389:0.523140:0.712389:0.000000 5:@0.532742:0.728240:0.548075:0.728240:0.548075:0.714525:0.532742:0.714525:0.000000 Recuerda que el perímetro del rectángulo está dado por :@0.514231:0.756158:0.930612:0.756158:0.930612:0.739724:0.514231:0.739724:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la suma de todos sus lados.:@0.514231:0.772800:0.711211:0.772800:0.711211:0.756366:0.514231:0.756366:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Luego :@0.514231:0.795874:0.564327:0.795874:0.564327:0.779440:0.514231:0.779440:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.698255:0.795874:0.705710:0.795874:0.705710:0.779468:0.698255:0.779468:0.000000 2 2 48:@0.705643:0.795874:0.842221:0.795874:0.842221:0.779440:0.705643:0.779440:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.707863:0.795320:0.723197:0.795320:0.723197:0.781604:0.707863:0.781604:0.000000 x:@0.734228:0.795874:0.741683:0.795874:0.741683:0.779468:0.734228:0.779468:0.000000 1 1:@0.743836:0.795320:0.786240:0.795320:0.786240:0.781604:0.743836:0.781604:0.000000:0.000000:0.000000 x:@0.761298:0.795874:0.768753:0.795874:0.768753:0.779468:0.761298:0.779468:0.000000 :@0.786148:0.795874:0.790179:0.795874:0.790179:0.779440:0.786148:0.779440:0.000000 x:@0.797278:0.795874:0.804733:0.795874:0.804733:0.779468:0.797278:0.779468:0.000000 5 :@0.806879:0.795320:0.826722:0.795320:0.826722:0.781604:0.806879:0.781604:0.000000:0.000000 6 48:@0.788352:0.822166:0.842228:0.822166:0.842228:0.805732:0.788352:0.805732:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.797259:0.822166:0.804714:0.822166:0.804714:0.805760:0.797259:0.805760:0.000000 5:@0.806868:0.821611:0.822201:0.821611:0.822201:0.807895:0.806868:0.807895:0.000000 6:@0.771032:0.848563:0.780015:0.848563:0.780015:0.832130:0.771032:0.832130:0.000000 x:@0.779941:0.848563:0.787396:0.848563:0.787396:0.832157:0.779941:0.832157:0.000000 6:@0.774732:0.866107:0.783715:0.866107:0.783715:0.849673:0.774732:0.849673:0.000000 :@0.793598:0.855371:0.815091:0.855371:0.815091:0.838938:0.793598:0.838938:0.000000:0.000000:0.000000 5:@0.795818:0.854817:0.811152:0.854817:0.811152:0.841101:0.795818:0.841101:0.000000 48:@0.818804:0.848563:0.836696:0.848563:0.836696:0.832130:0.818804:0.832130:0.000000:0.000000 6:@0.823259:0.866107:0.832241:0.866107:0.832241:0.849673:0.823259:0.849673:0.000000 x 8 m:@0.786787:0.881662:0.842227:0.881662:0.842227:0.865228:0.786787:0.865228:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.796824:0.881107:0.812157:0.881107:0.812157:0.867391:0.796824:0.867391:0.000000 Por tanto, ancho 8m :@0.514231:0.905451:0.680863:0.905451:0.680863:0.889017:0.514231:0.889017:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.635453:0.904896:0.650786:0.904896:0.650786:0.891181:0.635453:0.891181:0.000000 largo 2(8 m):@0.739178:0.905451:0.842249:0.905451:0.842249:0.889017:0.739178:0.889017:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.778328:0.904896:0.793661:0.904896:0.793661:0.891181:0.778328:0.891181:0.000000 5:@0.787922:0.928686:0.803255:0.928686:0.803255:0.914970:0.787922:0.914970:0.000000 16 m:@0.803163:0.929241:0.842236:0.929241:0.842236:0.912807:0.803163:0.912807:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.762966:0.667759:0.771949:0.667759:0.771949:0.651325:0.762966:0.651325:0.000000 x:@0.771876:0.667759:0.779330:0.667759:0.779330:0.651353:0.771876:0.651353:0.000000 x:@0.679618:0.706590:0.687073:0.706590:0.687073:0.690184:0.679618:0.690184:0.000000 DBA 9 (Ev. 3) Realiza combinaciones de operaciones, encuentra propiedades y resuelve ecuaciones en donde están involucradas.:@0.083863:0.971354:0.760376:0.971354:0.760376:0.959402:0.083863:0.959402:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000