Question

Find all real solutions of the equation by using the square root method.(z−8)2=5z=

Answer 1

Answer:

$z=8+\sqrt{5},8-\sqrt{5}$

Explanation:

Given the equation:

$(z-8)^2=5$

First, take the square root of both sides:

$\begin{gathered} (z-8)^2=5 \\ \sqrt{(z-8)^2}=\pm\sqrt{5} \\ z-8=\pm\sqrt{5} \end{gathered}$

Next, add 8 to both sides of the equation:

$\begin{gathered} z-8+8=8\pm\sqrt{5} \\ \implies z=8\pm\sqrt{5} \end{gathered}$

Solve for all the real solutions:

$z=8+\sqrt{5}\text{ or }z=8-\sqrt{5}$

The real solutions to the equation are:

$\begin{gathered} z=8+\sqrt{5} \\ z=8-\sqrt{5} \end{gathered}$