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SSC CGL 2023 PYQ — Question 52

SSC CGL - 17 July 2023 - Shift 3 • Quantitative Aptitude • Q52

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If x + 1x\frac{1}{x} = −6, what will be the value of x5 + 1x5\frac{1}{x^5}?

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Correct answer: B

Explanation

The correct answer is Option 2 i.e. -6726.

Now, according to the question

⇒ x + 1/x = -6

squaring both sides

⇒ x2 + 1/x2 = (-6)2 - 2

⇒ x2 + 1/x2 = 34

If x + 1/x = c then, x3 + 1/x3 = c3 - 3c

⇒ x3 + 1/x3 = (-6)3 - 3 × -6

⇒ x3 + 1/x3 = -216 + 18 = -198

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

⇒ 34 × -198 - (-6)

⇒ -6732 + 6 = -6726