What are the solutions to the equation (x^2)^3=x ?

The solutions to the equation (x^2)^3=x are x=0,x=1

Find the zeros of (x^2)^3=x

The zeros of (x^2)^3=x are x=0,x=1

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(x^{2})^{3} = x

x = 0, x = 1

Solution steps

(x^{2})^{3} = x

Expand

(x^{2})^{3} : x^{6}

x^{6} = x

Move

x

to the left side

x^{6} - x = 0

Factor

x^{6} - x : x (x - 1) (x^{4} + x^{3} + x^{2} + x + 1)

x (x - 1) (x^{4} + x^{3} + x^{2} + x + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 1 = 0 or x^{4} + x^{3} + x^{2} + x + 1 = 0

Solve

x - 1 = 0 : x = 1

Solve

x^{4} + x^{3} + x^{2} + x + 1 = 0 :

No Solution for

x \in R

The solutions are

x = 0, x = 1

16 x^{4} - 1 = 0

5 x^{3} = - 45 x

x^{4} - 64 = 0

8 x^{3} - 125 = 0

a^{3} = 216

What are the solutions to the equation (x^2)^3=x ?
The solutions to the equation (x^2)^3=x are x=0,x=1
Find the zeros of (x^2)^3=x
The zeros of (x^2)^3=x are x=0,x=1