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SSC CGL 2023 PYQ — Question 60

SSC CGL - 27 July 2023 - Shift 3 • Quantitative Aptitude • Q60

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If (x+1x)=6\left(x + \frac{1}{x}\right)=6, and x > 1, find the value of (x2−1x2).\left(x^2 - \frac{1}{x^2}\right).

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 24224\sqrt{2}.

(x+1x)=6\left(x + \frac{1}{x}\right)=6                       .................(1)

let a = 6

and x - 1/x = a2−4 \sqrt{a^2 - 4} = 36−4\sqrt{36-4} = 32 \sqrt{32} = 42 \sqrt{2}               .......................(2)

Multiply equations 1 and 2

⇒ (x + 1/x) (x - 1/x) = 6 ×  42 \sqrt{2} 

⇒ (x + 1/x) (x - 1/x) = 242 \sqrt{2}

⇒ x2 - 1/x2 =  242 \sqrt{2}