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

Question

Quizplus · Accepted Answer

To solve the equation $\sqrt { x + 6 } + \sqrt { 2 - x } = 4$, we can square both sides to eliminate the square roots, and then isolate x. However, the correct approach involves recognizing that the domain of both square root functions must be considered. For $\sqrt { x + 6 }$, $x \geq -6$, and for $\sqrt { 2 - x }$, $x \leq 2$. After squaring both sides and simplifying, we find that $x = -2$ is the only solution that satisfies both the original equation and the domain restrictions. Other potential solutions do not satisfy the original equation when substituted back in.

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

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