The number of roots of the equation 2√(2x+1)=2x-1 is equal to

Correct answer: (B) 1. LHS is always non negative. So, RHS also has to be the same So, x≥1/2. Squaring both sides, we get, 42x+1=2x-1^2=4x^2+1-4x 4x^2-12x-3=0⇒x=(12±√(144+48))/(2×4) x=(3±√(9+3))/2=(3±2√3)/2 ⇒x=(3+2√3)/2 as x>1/2

Q2 / 82 · NTA Abhyas (JEE Main) 2020 · Mathematics · Quadratic Equation

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

A
$0$
Correct answer
B
$1$
C
$2$
D
$3$

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,
$4 (2 x + 1) = {(2 x - 1)}^{2} = 4 x^{2} + 1 - 4 x$
$4 x^{2} - 12 x - 3 = 0 \Rightarrow x = \frac{12 \pm \sqrt{144 + 48}}{2 \times 4}$
$x = \frac{3 \pm \sqrt{9 + 3}}{2} = \frac{3 \pm 2 \sqrt{3}}{2}$
$\Rightarrow x = \frac{3 + 2 \sqrt{3}}{2} (as x > \frac{1}{2})$

Hence, the correct answer is option: 'B'.

The number of roots of the equation 22x+1=2x-1 is equal to

Solution

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