Question

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

Answer 1

`z=8+√(5),8-√(5)`

Step-by-step explanation:

Given the equation:

`(z-8)^2=5`

First, take the square root of both sides:

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

Next, add 8 to both sides of the equation:

`\begin{gathered} z-8+8=8\pm√(5) \\ \implies z=8\pm√(5) \end{gathered}`

Solve for all the real solutions:

`z=8+√(5)\text{ or }z=8-√(5)`

The real solutions to the equation are:

`\begin{gathered} z=8+√(5) \\ z=8-√(5) \end{gathered}`