Chapter 12.1, Problem 27WE

To determine

To solve: The equation $r^2-22r+121=4$ and express irrational solution in simplest radical form.

Answer to Problem 27WE

The solution set is $\left(13,9\right)$ .

Explanation of Solution

Given information:

The given equation $r^2-22r+121=4$ .

Calculation:

  $\begin{array}{l}\Rightarrow r^2-22r+121=4\\ \Rightarrow {\left(r-11\right)}^2=4\\ \Rightarrow r-11=\pm \sqrt{4}\\ \Rightarrow r-11=\pm \sqrt{2^2}\\ \Rightarrow r-11=\pm 2\\ \Rightarrow r-11+11=11\pm 2\end{array}$

(Adding 11 on both sides)

  $\begin{array}{l}\Rightarrow r=11\pm 2\\ \Rightarrow r=13,r=9\end{array}$

Therefore, the solution set is $\left(13,9\right)$ .