# If x^3 = 1/4x, what is the possible value of x?

Jun 27, 2016

$x = 0 \mathmr{and} x = - \frac{1}{2} \mathmr{and} x = \frac{1}{2}$

#### Explanation:

Factorize the above equation to get the possible values of x.

${x}^{3} = \frac{1}{4} \cdot x$

=> $4 {x}^{3} = x$

=> $4 {x}^{3} - x = 0$

=> $x \left(4 {x}^{2} - 1\right) = 0$

=> $x \left(4 {x}^{2} - 1\right) = 0$

=> $x \left({\left(2 x\right)}^{2} - {\left(1\right)}^{2}\right) = 0$

=> $x \left(2 x + 1\right) \left(2 x - 1\right) = 0$

$x = 0 \mathmr{and} x = - \frac{1}{2} \mathmr{and} x = \frac{1}{2}$