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SSC CGL 2021 PYQ — Question 55

SSC CGL - 13 Aug 2021 - Shift 1 • Quantitative Aptitude • Q55

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If x + 1x\frac{1}{x} = 4, then the value of x5 + 1x5\frac{1}{x5} is:

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 724

⇒ x + 1/x = 4    (1)

Squaring both sides,

⇒ x2 + 1/x2 + 2 = 16

⇒ x2 + 1/x2 = 14

Cubing equation (1)

⇒ x3 + 1/x3 + 3(x + 1/x) = 64

⇒ x3 + 1/x3 + 3(4) = 64

⇒ x3 + 1/x3 = 64 - 12

⇒ 52

⇒ ( x3 + 1/x3)(x2 + 1/x2) = x5 + x + 1/x + 1/x5

⇒ 52 × 14 = x5 + 4 + 1/x5

⇒ x5 + 1/x5 = 728 - 4

⇒ 724