Question

Un posible valor de x que hace CIERTA la expresion∛(x^2)= x^2

Answer 1

(x^2)^(1/3) = x^2
x^2 = x^6
x = x^3 or x = -x^3
x-x^3 = 0 or x = -x^3
-x (x-1) (x+1) = 0 or x = -x^3
Multiplica por -1:
x (x-1) (x+1) = 0 or x = -x^3
x-1 = 0 or x = 0 or x+1 = 0 or x = -x^3
x = 1 or x = 0 or x = -1 or x = -x^3
x = 1 or x = 0 or x = -1 or x^3+x = 0
x = 1 or x = 0 or x = -1 or x (x^2+1) = 0
x = 1 or x = 0 or x = -1 or x = 0 or x^2+1 = 0
x = 1 or x = 0 or x = -1 or x = 0 or x^2 = -1
x^2 = -1 x no tiene solucion por que no pertece a lo reales en este caso , x^2 >=0 -1<0:
Rpta: |
| x = 1 or x = 0 or x = -1 or x = 0