Chapter 6, Problem 6CT

To determine

To Simplify:

Find the real roots of $2x^3=-16$ .

Answer to Problem 6CT

  $x=-2$

Explanation of Solution

Given :

The equation is :

  $2x^3=-16$

Calculation:

Given:

  $\begin{array}{l}2x^3=-16\\ \Rightarrow \frac{2x^3}{2}=\frac{-16}{2}\mathrm{..............}[\text{divide each side by 2]}\\ \Rightarrow x^3=-8\\ \Rightarrow \sqrt[3]{x^3}=\sqrt[3]{{\left(-2\right)}^3}\mathrm{........}[\text{take cube root each side]}\\ \Rightarrow x=-2\end{array}$