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  4. If x is a solution of the equation, √2x + 1 - √2x-1 = 1, (x ge (1/2) ), then √4x2 - 1 is equal to :

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Q. 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 :

JEE MainJEE Main 2016Complex Numbers and Quadratic Equations

Solution:

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