NTA Abhyas JEE Main2020MathematicsQuadratic EquationPractice

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

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Correct answer

B. 1

Step-by-step solution

LHS is always non negative. So, RHS also has to be the same So, x ≥ 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 ⇒ x = 12 ± 144 + 48 2 × 4 x = 3 ± 9 + 3 2 = 3 ± 2 3 2 ⇒ x = 3 + 2 3 2   as   x > 1 2

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