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SSC CGL 2023 PYQ — Question 73

SSC CGL - 18 July 2023 - Shift 3 • Quantitative Aptitude • Q73

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If (x + 1x\frac{1}{x}) = 5, what is the value of (x8 + 1x8\frac{1}{x^8})?

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Correct answer: A

Explanation

The correct answer is Option 1 i.e. 277727.

x + 1/x = 5

Squaring both sides

⇒ (x + 1/x)2 = 25

⇒ x2 + 1/x2 + 2 = 25

⇒ x2 + 1/x2 = 25 - 2

⇒ x2 + 1/x2 = 23

Squaring both sides

⇒ (x2 + 1/x2)2 = 232

⇒ x4 + 1/x4 + 2 = 529

⇒ x4 + 1/x4 = 527

Squaring both sides

⇒ (x4 + 1/x4)2 = 5272

⇒ x8 + 1/x8 + 2 = 277729

⇒ x8 + 1/x8 = 277727