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Question: The equation \(\sqrt{(x + 1)} - \sqrt{(x - 1)} = \sqrt{(4x - 1)}\), \(x \in R\)has...

The equation (x+1)−(x−1)=(4x−1)\sqrt{(x + 1)} - \sqrt{(x - 1)} = \sqrt{(4x - 1)}, x∈Rx \in Rhas

A

One solution

B

Two solution

C

Four solution

D

No solution

Answer

No solution

Explanation

Solution

Given (x+1)−(x−1)=(4x−1)\sqrt{(x + 1)} - \sqrt{(x - 1)} = \sqrt{(4x - 1)} .....(i)

Squaring both sides, we get, −2(x2−1)=2x−1- 2\sqrt{(x^{2} - 1)} = 2x - 1

Squaring again, we get, x=54,x = \frac{5}{4}, which does not satisfy

equation (i)

Hence, there is no solution of the given equation.