Question

If $\sqrt{x+1}-\sqrt{x-1}=1$, then $x$ is equal to

• A. $\frac{2}{3}$
• B. $\frac{4}{5}$
• C. $\frac{5}{4}$
• D. $\frac{3}{5}$

Answer 1

Answer: (C)

$\frac{5}{4}$

Given, $\sqrt{x+1}=1+\sqrt{x-1}$

Squaring both sides,
$\therefore x+1=1+x+2\left(\sqrt{x-1}\right)$

$\therefore 1=2\left(\sqrt{x-1}\right)$
Again squaring both sides,
$\therefore 1=4(x-1)$

$\therefore 4x-4-1=0\Rightarrow 4x$
$\therefore x=\frac{5}{4}$