Question

The number of roots of the equation $2\sqrt{2x+1}=2x-1$ is equal to

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

Answer: (B)

LHS is always non negative.
So, RHS also has to be the same
So, $x\ge \frac{1}{2}.$
Squaring both sides, we get,
$4\left(2x+1\right)={\left(2x-1\right)}^2=4x^2+1-4x$
$4x^2-12x-3=0\Rightarrow x=\frac{12\pm \sqrt{144+48}}{2\times 4}$
$x=\frac{3\pm \sqrt{9+3}}{2}=\frac{3\pm 2\sqrt{3}}{2}$
$\Rightarrow x=\frac{3+2\sqrt{3}}{2}\left(asx>\frac{1}{2}\right)$