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Identify all of the solutions of _______

Identify all of the solutions of _______-example-1
User Xiaogw
by
7.8k points

2 Answers

2 votes

Answer:

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

User Andrej Sramko
by
8.0k points
3 votes

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

User Matthieun
by
8.8k points

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