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

Question

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

Daniel Salas Mora · Accepted Answer

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

Find the solution (if any) to the equation. $x+1=3−x\sqrt { x + 1 } = 3 - \sqrt { x }$

A) $\frac { 16 } { 9 }$
B) $\frac { 2 } { 9 }$
C) $\frac { 4 } { 3 }$
D) $\frac { 32 } { 3 }$
E) no solution

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Find the solution (if any) to the equation. x+1=3−x\sqrt { x + 1 } = 3 - \sqrt { x }x+1​=3−x​ A) x=169x = \frac { 16 } { 9 }x=916​ B) x=29x = \frac { 2 } { 9 }x=92​ C) x=43x = \frac { 4 } { 3 }x=34​ D) x=323x = \frac { 32 } { 3 }x=332​ E) no solution

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Find the solution (if any) to the equation. $x+1=3−x\sqrt { x + 1 } = 3 - \sqrt { x }$

A) $\frac { 16 } { 9 }$
B) $\frac { 2 } { 9 }$
C) $\frac { 4 } { 3 }$
D) $\frac { 32 } { 3 }$
E) no solution