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 eaual to :

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

Answer 1

The correct option is B $\frac{3}{4}$

$\sqrt{2x+1}=1+\sqrt{2x–1}\text{Squaring both the sides,}2x+1=1+2x-1+2\sqrt{2x–1}\Rightarrow 1=2\sqrt{2x–1}\text{Squaring both the sides,}\Rightarrow 1=4(2x-1)\Rightarrow x=\frac{5}{8}\sqrt{4x^2–1}=\sqrt{4(\frac{5}{8}{)}^2–1}=\frac{3}{4}$