Chapter 6.7, Problem 3MRE

To determine

To Solve:

  $\sqrt{y^2+12}=2y$

Answer to Problem 3MRE

  $y=\pm 2$

Explanation of Solution

Given :

The equation is :

  $\sqrt{y^2+12}=2y$

Calculation:

Given:

  $\begin{array}{l}\sqrt{y^2+12}=2y\\ \Rightarrow {\left(\sqrt{y^2+12}\right)}^2={\left(2y\right)}^2\mathrm{......}[\text{square each side]}\\ \Rightarrow y^2+12=4y^2\\ \Rightarrow y^2+12-y^2=4y^2-y^2\mathrm{..}[{\text{subtract y}}^2\text{ from each side]}\\ \Rightarrow 3y^2=12\\ \Rightarrow \frac{3y^2}{3}=\frac{12}{3}\mathrm{......................}[\text{divide each side by 3]}\\ \Rightarrow y^2=4\\ \Rightarrow y=\pm \sqrt{4}\mathrm{.......................}[\text{take square root each side]}\\ \Rightarrow y=\pm 2\end{array}$