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Q.
The number of solutions of
$\sqrt{x+1}-\sqrt{x-1}=1 (x \in R )$
is
Complex Numbers and Quadratic Equations
Solution:
For the equation to make sense
we must have $x+1 \geq 0$ and $x-1 \geq 0 \Rightarrow x \geq-1, x \geq 1$
i.e. $x \geq 1$.
We rewrite equation as
$\sqrt{x+1}=1+\sqrt{x-1}$
and square both the sides to obtain
$x+1=1+x-1+2 \sqrt{x-1}$
$\Rightarrow \frac{1}{2}=\sqrt{x-1} \Rightarrow \frac{1}{4}=x-1 \text { or } x=\frac{5}{4}$
Also, $x=5 / 4$ satisfies the given equation.