Solve. Check for extraneous solutions.
-$( x - 6 ) ^ { 1 / 2 } = - 2$
A) $\{ 4 \}$
B) $\{ 10 \}$
C) $\{ 16 \}$
D) $ \varnothing $

Question

Quizplus · Accepted Answer

Taking the square root of both sides of the equation, we get:

$x-6 = (-2)^2$
$x-6 = 4$
$x = 10$

However, we need to check if this solution is an extraneous solution by plugging it back into the original equation:

$(10 - 6)^{1/2} = (-2)$

$4^{1/2} = -2$

$2 = -2$

This statement is false, so the solution $x = 10$ is extraneous. Therefore, the answer is D, indicating that there are no solutions to the equation.

Solve Check for Extraneous Solutions (x−6)1/2=−2( x - 6 ) ^ { 1 / 2 } = - 2(x−6)1/2=−2