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7/21/2019 Ar Answers Yahoo Com Question Index Qid 20060903121949AAAB4C
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la raiz cuadrada de tres es irracional?demostrar?demostrar por induccion matematica,
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Respuestas
Mejor respuesta: no se demuestra por induccionse demuestra por contradiccion
supon que raiz de 3 es racional, es decir, que3=p/q, donde p y q son enteros sin divisores comunes.eleva todo al cuadrado:3=p^2/q^23q^2=p^2
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Comentario
por lo tanto 3 divide a p^2, pero como 3 es primo eso quiere decir que 3 dividea p mismo, por lo tantop=3r, para algun numero r.entonces3q^2=p^2=(3r)^2=9r^2dividiendo por 3obtenemos queq^2=3r^2,lo que quiere decir que 3 divide a q^2, pero como 3 es primo entonces tieneque dividir a q mismo,
y aqui esta la contradiccion, pues encontramos que 3 es un divisor comun dep y q, pero nosotros habiamos supuesto que no tenian.....
locuaz hace 9 aos
4 0
Comentario
Basta quie uses tu calculadora....Irracional se considera a aquel nmero que tiene infinitos decimales, sin questos jams lleguen a tener un grupo de cifras un nmero peridico.
DANIELA GORRITO hace 9 aos
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La demostracin se hace por el absurdo, se plantea que si es racional,entonces se puede escribir como una fracin simplificada p/q. Luego sedemuestra que p y q deben ser pares. Entonces si son pares la fraccin noest simplificada ya que pueden dividirse los dos por 2 al menos. Pero lahiptesis es que se puede escribir como una fraccin simplificada, eso es unacontradiccin. El absurdo proviene de plantear que se puede escribir como unafraccin simple.
Un saludo, espero que lo puedas demostrar.yankenan hace 9 aos
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Hola la demostracion no se hace por induccion se hace por el absurdo de lasiguiente manera: Sup que 3 es racional entonces 3=p/q con p y q enterosy coprimos (es decir la fraccion no se puede simplificar mas, con esto no sepierde generalidad) entonces elevamos al cuadrado a ambos miembros yobtenemos que 3=(p/q) 2 entonces razonamos de la sig manera:
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1)3*q^2=p^2, bien ahora aplicando el teorema fundamental del algebra qfactorizamos p y q como producto de primos a potencias pero en este caso voa obviar las potencias pq aca es medio feo escribirlas jeje.2)P=p1*p2*...*pn y Q=q1*q2*...*qm; de esta manera tenemos3)3*(q1*...*qm)^2=(p1*...*pn)^2 entonces de esta manera como la factorizacionde un numero es unica y 3 es primo tenemos que del lado izquierdo de laigualdad el nmero 3 aparece una cantidad impar de veces en la factorizaciony del lado derecho una cantidad par lo cual esto es un absurdo. De estamanera demostramos que 3 no es un numero racional. Espero que te hayaservido
Alejandro Q hace 9 aos
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Si quieres te enseo clculo pero cobro 50 dolares la hora.
Israel H hace 9 aos
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por raiz de 3 en tu calculadora, notaras que despues del punto, los numerosno se repiten, o no tienen una secuencia (Pej 1.111111111111.... ,1.2123212321232123..., 3,5454545454...), s ino que tiene esta forma1,7320508075688772935274463415059, es decir no lo puedes expresar comoun fraccionario
I r hace 9 aos
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Hace tu tarea nene y dejate de joder a los demas con tus preguntas. Anda aestudiar, haraganote.
EX-BRAD PITT hace 9 aos
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la raiz cuadrada de tres es irracional?demostrar?
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