The number of solutions of √x+1-√x-1=1 (x ∈ R ) is

Question

The number of solutions of √x+1-√x-1=1 (x ∈ R ) is (A) 1 (B) 2 (C) 4 (D) infinite

Tardigrade Admin · Accepted Answer

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

x + 1 = 1 + x - 1

and square both the sides to obtain

x + 1 = 1 + x - 1 + 2 x - 1

\Rightarrow \frac{1}{2} = x - 1 \Rightarrow \frac{1}{4} = x - 1 or x = \frac{5}{4}

Also,

x = 5/4

satisfies the given equation.

Q. The number of solutions of x+1​−x−1​=1(x∈R) is