Question

Identify all of the solutions of _______

Answer 1

x = 8 and x = 9

Explanation:

`√(x - 8) + 8 = x`

Isolate the radical and square both sides.

`√(x - 8) = x - 8`

`(√(x - 8))^2 = (x - 8)^2`

`x - 8 = x^2 - 16x + 64`

`x^2 - 17x + 72 = 0`

`(x - 8)(x - 9) = 0`

`x - 8 = 0~~~or~~~x - 9 = 0`

`x = 8~~~or~~~x = 9`

Since squaring both sides may introduce extraneous solutions, we check both of our solutions in the original equation.

Check x = 8:

`√(8 - 8) + 8 = 8`

`√(0) + 8 = 8`

`0 + 8 = 8`

`8 = 8`

8 = 8 is a true statement, so x = 8 is a solution.

Check x = 9:

`√(9 - 8) + 8 = 9`

`√(1) + 8 = 9`

`1 + 8 = 9`

`9 = 9`

9 = 9 is a true statement, so x = 9 is a solution.

Answer: x = 8 and x = 9

Answer 2

the answer is the third, you can substitute the option to verify the solution