Find the solution (if any)to the equation. $\sqrt { x + 1 } = 3 - \sqrt { x }$
A) $x = \frac { 16 } { 9 }$
B) $x = \frac { 2 } { 9 }$
C) $x = \frac { 4 } { 3 }$
D) $x = \frac { 32 } { 3 }$
E)no solution

Question

Quizplus · Accepted Answer

To solve the equation $\sqrt { x + 1 } = 3 - \sqrt { x }$, square both sides to eliminate the square roots: $(\sqrt { x + 1 })^2 = (3 - \sqrt { x })^2$, which simplifies to $x + 1 = 9 - 6\sqrt { x } + x$. Rearranging gives $6\sqrt { x } = 8$, and squaring both sides again gives $36x = 64$, so $x = \frac { 64 } { 36 } = \frac { 16 } { 9 }$.

Find the Solution (If Any)to the Equation x+1=3−x\sqrt { x + 1 } = 3 - \sqrt { x }x+1​=3−x​

Find the Solution (If Any)to the Equation $\sqrt { x + 1 } = 3 - \sqrt { x }$