Solve the radical equation, and check all proposed solutions.
-$$\sqrt { x + 6 } + \sqrt { 2 - x } = 4$$
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 first isolate one of the square roots and then square both sides to eliminate the square root, followed by solving the resulting equation. After squaring both sides and simplifying, we find that $x = -2$ is a solution. Checking $x = -2$ in the original equation, it satisfies the equation, making it the correct solution. Other proposed solutions do not satisfy the original equation when checked.

Solve the Radical Equation, and Check All Proposed Solutions x+6+2−x=4\sqrt { x + 6 } + \sqrt { 2 - x } = 4x+6​+2−x​=4

Solve the Radical Equation, and Check All Proposed Solutions $\sqrt { x + 6 } + \sqrt { 2 - x } = 4$