Chapter 12.1, Problem 31WE

To determine

To solve: The equation $\frac{1}{5}{r}^2-2=\frac{5}{6}$ and express irrational solution in simplest radical form.

Answer to Problem 31WE

The solution set is $\left(\sqrt{\frac{85}{6}},-\sqrt{\frac{85}{6}}\right)$ .

Explanation of Solution

Given information:

The given equation $\frac{1}{5}{r}^2-2=\frac{5}{6}$ .

Calculation:

  $\begin{array}{l}\Rightarrow \frac{1}{5}{r}^2-2=\frac{5}{6}\\ \Rightarrow \frac{1}{5}{r}^2-2+2=\frac{5}{6}+2\end{array}$

(Adding 2 on both sides)

  $\begin{array}{l}\Rightarrow \frac{1}{5}{r}^2=\frac{17}{6}\\ \Rightarrow \frac{1\cdot 5}{5}{r}^2=\frac{17\cdot 5}{6}\end{array}$

(Multiply by 5 on both sides)

  $\begin{array}{l}\Rightarrow r^2=\frac{85}{6}\\ \Rightarrow r=\pm \sqrt{\frac{85}{6}}\\ \Rightarrow r^2=\frac{85}{6}\\ \Rightarrow r=\pm \sqrt{\frac{85}{6}}\\ \Rightarrow r=\sqrt{\frac{85}{6}},r=-\sqrt{\frac{85}{6}}\end{array}$

Therefore, the solution set is $\left(\sqrt{\frac{85}{6}},-\sqrt{\frac{85}{6}}\right)$ .