Question

Solve x^3 - 125 =0 complex roots

Answer 1

ANSWER:

$x=5,-\frac{5}{2}+\frac{5\sqrt[]{3}}{2}i,-\frac{5}{2}-\frac{5\sqrt[]{3}}{2}i$

STEP-BY-STEP EXPLANATION:

We have the following equation:

$\begin{gathered} x^3\: -\: 125\: =0\: \\ x^3\: \: =125\: \end{gathered}$

Solving for x:

$\begin{gathered} x=\sqrt[3]{125} \\ x_1=5 \\ x_2=\sqrt[3]{125}\cdot\frac{-1+\sqrt[]{3}}{2}i=5\cdot\frac{-1+\sqrt[]{3i}}{2}=-\frac{5}{2}+\frac{5\sqrt[]{3}}{2}i \\ x_3=\sqrt[3]{125}\cdot\frac{-1-\sqrt[]{3}}{2}i=5\cdot\frac{-1-\sqrt[]{3i}}{2}=-\frac{5}{2}-\frac{5\sqrt[]{3}}{2}i \end{gathered}$