Solve the equation.
-$\sqrt { x + 6 } + \sqrt { 2 - x } = 4$
A) $\{ \sqrt { 31 } , - 2 \}$
B) $\{ 2 , - 2 \}$
C) $\{ - 2 \}$
D) $\{ 0 \}$

Question

Quizplus · Accepted Answer

To solve the equation $\sqrt { x + 6 } + \sqrt { 2 - x } = 4$, we square both sides to eliminate the square roots, leading to a quadratic equation. After simplifying and solving the quadratic equation, we find that $x = -2$ is the only solution that satisfies the original equation when substituted back, as it keeps both expressions under the square roots non-negative. Other solutions from the quadratic equation might not satisfy the original equation due to the constraints imposed by the square roots.

Solve the Equation x+6+2−x=4\sqrt { x + 6 } + \sqrt { 2 - x } = 4x+6​+2−x​=4

Solve the Equation $\sqrt { x + 6 } + \sqrt { 2 - x } = 4$