Chapter 12, Problem 2CR

To determine

To define: The correct option of expression ${\left(a-25\right)}^2=9$ and the options are,

  $\begin{array}{l}\text{a}.\left\{22,28\right\}\\ \text{b}\text{.}\left\{2,-8\right\}\\ \text{c}.\left\{2,-2\right\}\\ \text{d}\text{.}\text{}\left\{2,8\right\}\end{array}$

Answer to Problem 2CR

The correct option of expression ${\left(a-25\right)}^2=9$ is $\text{a}.\left\{22,28\right\}$ .

Explanation of Solution

Given information:

The expression ${\left(a-25\right)}^2=9$ and provided options are,

  $\begin{array}{l}\text{a}.\left\{22,28\right\}\\ \text{b}\text{.}\left\{2,-8\right\}\\ \text{c}.\left\{2,-2\right\}\\ \text{d}\text{.}\text{}\left\{2,8\right\}\end{array}$

The provided expression is ${\left(a-25\right)}^2=9$ now solve for the value of $x$ .

Take under root on both sides of equation,

  $\sqrt{{\left(a-25\right)}^2}=\pm \sqrt{9}$

Furthermore,

  $\left(a-25\right)=\pm 3$

Add 25 on both side of the equation,

  $\begin{array}{l}a-25+25=\pm 3+25\\ a=\pm 3+25\end{array}$

First take 3 as positive and solve,

  $\begin{array}{c}a=3+25\\ =28\end{array}$

Now, take 3 as negative and solve,

  $\begin{array}{c}a=-3+25\\ =22\end{array}$

The value of $a$ is $\left\{22,28\right\}$ .

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