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SSC CGL 2025 PYQ — Question 55

SSC CGL - 22 Sep 2025 - Shift 1 • Quantitative Aptitude • Q55

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Given, x+1x=5x + \frac{1}{x} = 5, then determine the value of 2xx2−1\frac{2x}{x^2 - 1}:

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 22121\frac{2\sqrt{21}}{21}.

x+1x=5x + \frac{1}{x} = 5

⇒ (x+1x)2=x2+1x2+2=52=25\left(x + \frac{1}{x}\right)^2 = x^2 + \frac{1}{x^2} + 2 = 5^2=25

⇒ x2+1x2=23x^2 + \frac{1}{x^2} = 23

⇒ (x−1x)2=x2+1x2−2\left(x - \frac{1}{x}\right)^2 = x^2 + \frac{1}{x^2} -2

⇒ (x−1x)2=23−2=21\left(x - \frac{1}{x}\right)^2 = 23 - 2 = 21

⇒ x−1x=21x - \frac{1}{x} = \sqrt{21}

⇒ 2x−1x=221=22121\frac{2}{x - \frac{1}{x}} = \frac{2}{\sqrt{21}}=\frac{2\sqrt{21}}{21}