# How do you solve the equation and identify any extraneous solutions for (3x^3)/4=192?

Jun 6, 2015

Multiply both sides by $\frac{4}{3}$ to get:

${x}^{3} = 256 = {2}^{8}$

This has one real solution:

$x = {2}^{\frac{8}{3}} = 4 \sqrt[3]{4}$

In case you are curious, the other two complex roots are:

$4 \omega \sqrt[3]{4}$ and $4 {\omega}^{2} \sqrt[3]{4}$

where $\omega = - \frac{1}{2} + \frac{\sqrt{3}}{2} i$

is called the primitive cube root of unity.

$\omega$ features in general solutions of cubic equations.