Question

If $x$ is a solution of the equation, $\sqrt{2x+1}-\sqrt{2x-1}=1,(x\ge \frac{1}{2})$, then $\sqrt{4x^2-1}$ is equal to:

• A. $\frac{3}{4}$
• B. $\frac{1}{2}$
• C. $2\sqrt{2}$
• D. $2$

Answer 1

Answer: (A)

$\frac{3}{4}$

$\sqrt{2x+1}-\sqrt{2x-1}=1$ ..... (1)

$\Rightarrow 2x+1+2x-1-2\sqrt{4x^2-1}=1$

$\Rightarrow 4x-1=2\sqrt{4x^2-1}$

$\Rightarrow 16x^2-8x+1=16x^2-4$

$\Rightarrow 8x=5$

$\Rightarrow x=\frac{5}{8}$ which satisfies equation $\left(1\right)$

So, $\sqrt{4x^2-1}=\frac{3}{4}$