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SSC CGL 2023 PYQ — Question 69

SSC CGL - 14 July 2023 - Shift 4 • Quantitative Aptitude • Q69

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If x > 0, and x4 + 1x4\frac{1}{x^4} = 254, what is the value of x5 + 1x5\frac{1}{x^5}?

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 7172717 \sqrt2.

Given that

⇒ x4 + 1x4\frac{1}{x^4} = 254 

⇒ (x2 + 1/x2)2 - 2 = 254

⇒ (x2 + 1/x2)2 = 256 

x2 + 1/x2  = 16

⇒ (x + 1/x)2 - 2 = 16

⇒ (x + 1/x)2 = 18

⇒ x + 1/x = 3√2

Cubing both sides

⇒ x3 + 1/x3 = 54√2 - 9√2 = 45√2

As we know,

⇒  x5 + 1x5\frac{1}{x^5}  = (x2 + 1x2\frac{1}{x^2}) (x3 + 1/x3) - (x + 1/x) = 16 × 45√2 - 3√2 = 720√2 - 3√2 = 717√2