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

$\sqrt{2x+1}-\sqrt{2x-1}=1\Rightarrow \sqrt{2x+1}=1+\sqrt{2x-1}\Rightarrow 2x+1=1+2x-1+2\sqrt{2x-1}$$\Rightarrow 1=2\sqrt{2x-1}\Rightarrow 1=4(2x-1)\Rightarrow 2x-1=\frac{1}{4}\Rightarrow 2x=\frac{5}{4}\Rightarrow x=\frac{5}{8}$

$\sqrt{4x^2-1}=\sqrt{4{(5/8)}^2-1}=\sqrt{25/16-1}=3/4$