Chapter 12, Problem 1CR

To determine

To define: The correct option of expression $2x^2-128=0$ and the options are,

  $\begin{array}{l}\text{a}.\left\{64\right\}\\ \text{b}\text{.}\left\{64,-64\right\}\\ \text{c}.\left\{8\right\}\\ \text{d}\text{.}\text{}\left\{8,-8\right\}\end{array}$

Answer to Problem 1CR

The correct option of expression $2x^2-128=0$ is $\text{d}\text{.}\text{}\left\{8,-8\right\}$ .

Explanation of Solution

Given information:

The expression $2x^2-128=0$ and provided options are,

  $\begin{array}{l}\text{a}.\left\{64\right\}\\ \text{b}\text{.}\left\{64,-64\right\}\\ \text{c}.\left\{8\right\}\\ \text{d}\text{.}\text{}\left\{8,-8\right\}\end{array}$

The provided expression is $2x^2-128=0$ now solve for the value of $x$ .

Add 128 both side in the equation,

  $\begin{array}{c}2x^2-128+128=128\\ 2x^2=128\end{array}$

Divided by 2 in the both side of equation,

  $\begin{array}{c}\frac{2x^2}{2}=\frac{128}{2}\\ x^2=64\end{array}$

Take under root on both sides of equation,

  $\begin{array}{c}\sqrt{x^2}=\pm \sqrt{64}\\ x=\pm 8\end{array}$

The value of $x$ is $\pm 8$ .

Thus, the option $\text{d}$ is correct.