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SSC CGL 2022 PYQ — Question 72

SSC CGL - 18 April 2022 - Shift 1 • Quantitative Aptitude • Q72

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If x2+1x2x^2+\frac{1}{x^2} = 23, x > 0 what is the value of x3+1x3x^3+\frac{1}{x^3} = ?

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 110

Formula used:

(a + b)2 = a2 + b2 + 2ab

(a + b)3 = a3 + b3 + 3ab(a + b)

Calculations:

Using the formula, we get

⇒ (x + 1/x)2 = x2 + 1/x2 + 2

⇒ (x + 1/x)2 = 23 + 2 = 25

⇒ (x + 1/x) = 5

Now,

(x + 1/x)3 = x3 + 1/x3 + 3(x + 1/x)

⇒ 53 = x3 + 1/x3 + 3 × 5

⇒ 125 - 15 = x3 + 1/x3

⇒ x3 + 1/x3 = 110