If x is a solution of √2x+1-√2x-1=1, x12, then 4x^2-1 is equal to:

Question

If $x$ is a solution of $\sqrt{2x+1}-\sqrt{2x-1}=1$, $x\ge\dfrac12$, then $4x^2-1$ is equal to:

Accepted Answer

Squaring: $4x-2\sqrt{4x^2-1}=1 \implies \sqrt{4x^2-1}=\dfrac{4x-1}2$, squaring again gives $16x^2-4=16x^2-8x+1 \implies x=\dfrac58$.

$$4x^2-1=4\left(\frac{25}{64}\right)-1=\frac34.$$

Solutions · 1