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SSC CGL 2021 PYQ — Question 62

SSC CGL - 18 Aug 2021 - Shift 2 • Quantitative Aptitude • Q62

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If x−1x=77x - \frac{1}{x}= \sqrt{77}, then one of the values of x3+1x3x^3+\frac{1}{x^3} is:

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Correct answer: B

Explanation

 The correct answer is option 2 i.e. 702

⇒ x−1x=77x - \frac{1}{x}= \sqrt{77}

on squaring both sides we get,

⇒ x2 + (1/x2) - 2 = 77

On adding 2 both sides we get,

⇒ (x + 1/x)2 = 77 + 4

⇒ (x + 1/x) = 9

On cubing both sides,

⇒ x3 + 1/x3 + 3(x + 1/x) = 729.

⇒ x3+1x3x^3+\frac{1}{x^3}= 729 - 27 = 702.