Solve the equation.
-$$( 2 x + 3 ) ^ { 1 / 2 } + ( 4 - x ) ^ { 1 / 2 } = 4$$
A) $\varnothing$
B) $\{ 3 \}$
C) $\left\{ 3 , \frac { 11 } { 9 } \right\}$
D) $\{ - 3 \}$

Question

Quizplus · Accepted Answer

To solve the equation $(2x + 3)^{1/2} + (4 - x)^{1/2} = 4$, we square both sides to eliminate the square roots, leading to a quadratic equation. After simplifying and solving the quadratic equation, we find two solutions: $x = 3$ and $x = \frac{11}{9}$. Both solutions satisfy the original equation when substituted back, confirming they are correct.

Solve the Equation (2x+3)1/2+(4−x)1/2=4( 2 x + 3 ) ^ { 1 / 2 } + ( 4 - x ) ^ { 1 / 2 } = 4(2x+3)1/2+(4−x)1/2=4

Solve the Equation $( 2 x + 3 ) ^ { 1 / 2 } + ( 4 - x ) ^ { 1 / 2 } = 4$