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Q.
The number of roots of the equation $2\sqrt{2 x + 1}=2x-1$ is equal to
NTA AbhyasNTA Abhyas 2020Complex Numbers and Quadratic Equations
Solution:
LHS is always non negative.
So, RHS also has to be the same
So, $x\geq \frac{1}{2}.$
Squaring both sides, we get,
$4\left(2 x + 1\right)=\left(2 x - 1\right)^{2}=4x^{2}+1-4x$
$4x^{2}-12x-3=0\Rightarrow x=\frac{12 \pm \sqrt{144 + 48}}{2 \times 4}$
$x=\frac{3 \pm \sqrt{9 + 3}}{2}=\frac{3 \pm 2 \sqrt{3}}{2}$
$\Rightarrow x=\frac{3 + 2 \sqrt{3}}{2}\left(as x > \frac{1}{2}\right)$