Question

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

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

Answer 1

Answer: (A)

$\sqrt{2x+1}=1+\sqrt{2x-1}$
Squaring on both sides
$2x+1=1+2x-1+2\sqrt{2x-1}$
$1=2\sqrt{2x-1}$
$1=4(2x-1)$
$x=5/8$
Now $\sqrt{4x^2-1}$ at $x=5/8$
$=\sqrt{4\times \frac{25}{64}-1}=3/4$