What are the solutions to the equation 3x^3=x ?

The solutions to the equation 3x^3=x are x=0,x=-1/(sqrt(3)),x= 1/(sqrt(3))

Find the zeros of 3x^3=x

The zeros of 3x^3=x are x=0,x=-1/(sqrt(3)),x= 1/(sqrt(3))

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3 x^{3} = x

x = 0, x = - \frac{1}{3}, x = \frac{1}{3}

Decimal Notation

x = 0, x = - 0.57735 \dots, x = 0.57735 \dots

Solution steps

3 x^{3} = x

Move

x

to the left side

3 x^{3} - x = 0

Factor

3 x^{3} - x : x (3 x + 1) (3 x - 1)

x (3 x + 1) (3 x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 3 x + 1 = 0 or 3 x - 1 = 0

Solve

3 x + 1 = 0 : x = - \frac{1}{3}

Solve

3 x - 1 = 0 : x = \frac{1}{3}

The solutions are

x = 0, x = - \frac{1}{3}, x = \frac{1}{3}

(x + 5)^{2} (x - 2) = 0

z^{3} = - 1 + i

5 z^{3} + 13 z^{2} = 28 z

x^{3} - 6 x^{2} + 33 x - 92 = 0

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

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