solve x^3-x=0 — step-by-step solution

Let's solve in

ℝ

x^{3} - x = 0

You can write the expression:

x^{3} - x

in factored form:

x \cdot (x^{2} - 1)

A product is zero if and only if one of its factors is zero: we solve each factor equal to 0

⇥Let's solve in

ℝ

x = 0

⇥Solution found:

x = 0

⇥Let's solve in

ℝ

x^{2} - 1 = 0

⇥The two numbers whose square is

1

are

-1

and

1

⇥Solutions obtained:

x = {-1, 1}

▶Solution:

x = {-1, 0, 1}