If √x-1-√x+1+1=0, then 4x equals:

1957 AMC 12 Problem 22

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22.

\sqrt{x-1}-\sqrt{x+1}+1=0,

then

4x

equals:

5

4\sqrt{-1}

0

1\frac14

no real value

Rearrange to

\sqrt{x+1}=\sqrt{x-1}+1

After squaring once, isolate

\sqrt{x-1}

Rearrange and square:

\begin{aligned} \sqrt{x+1}&=\sqrt{x-1}+1,\\ x+1&=x-1+2\sqrt{x-1}+1. \end{aligned}

Thus

2\sqrt{x-1}=1,

x-1=\frac{1}{4}

and

x=\frac{5}{4}.

This value satisfies the original equation. Therefore

4x=5.

Thus, the correct answer is A.