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JEE Main 201610 AprilOnline
Exam
JEE Main
Year
2016
Date
10 April
Mode
Online
Subject
Mathematics
Chapter
Quadratic Equation

JEE Main 2016 · 10 April · Online · Mathematics · Quadratic Equation

If x is a solution of the equation 2x + 1 - 2x - 1 = 1, (x ≥...

If xx is a solution of the equation 2x+1−2x−1=1,\sqrt{2x + 1} - \sqrt{2x - 1} = 1,\left(x \ge \dfrac{1}{2}\right),then, then\sqrt{4{x}^{2} - 1} is equal to :

Options

  1. A34\dfrac{3}{4}
  2. B12\dfrac{1}{2}
  3. C222\sqrt{2}
  4. D22

Correct answer

A. 34\dfrac{3}{4}

Step-by-step solution

2x+1−2x−1=1...(1)</p><p>\sqrt{2x + 1} - \sqrt{2x - 1} = 1 . . . \left(1\right)</p><p>⇒ 2x + 1 + 2x - 1 - 2\sqrt{4{x}^{2} - 1} = 1</p><p></p><p>⇒ 4x - 1 = 2\sqrt{4{x}^{2} - 1}</p><p></p><p>⇒ 16{x}^{2} - 8x + 1 = 16{x}^{2} - 4</p><p></p><p>⇒ 8x = 5</p><p></p><p>⇒ x = 58whichsatisfiesequation(1).</p><p>So,\dfrac{5}{8} which satisfies equation \left(1\right).</p><p>So,\sqrt{4{x}^{2} - 1} = 34</p>\dfrac{3}{4}</p>

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