Question

Identify all of the solutions of _______

Answer 1

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

Answer 2

Answer:

x = 8 and x = 9

Step-by-step explanation:

$\sqrt{x - 8} + 8 = x$

Isolate the radical and square both sides.

$\sqrt{x - 8} = x - 8$

$(\sqrt{x - 8})^2 = (x - 8)^2$

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

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

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

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

$x = 8~~~or~~~x = 9$

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

Check x = 8:

$\sqrt{8 - 8} + 8 = 8$

$\sqrt{0} + 8 = 8$

$0 + 8 = 8$

$8 = 8$

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

Check x = 9:

$\sqrt{9 - 8} + 8 = 9$

$\sqrt{1} + 8 = 9$

$1 + 8 = 9$

$9 = 9$

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

Answer: x = 8 and x = 9