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SSC CGL 2021 PYQ — Question 65

SSC CGL - 13 Aug 2021 - Shift 3 • Quantitative Aptitude • Q65

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If 2x2 - 8x - 1 = 0, then what is the value of 8x3−1x38x^3 - \frac{1}{x^3}?

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 560

⇒ 2x2 - 8x - 1 = 0

⇒ 2x2 - 1 = 8x

⇒ 2x - 1/x = 8

⇒ (a - b)3 = a3 - b3 - 3ab(a - b)

⇒ a = 2x, and b = 1/x

⇒ (2x - 1/x)3 = 8x3 - 1/x3 - 3(2x)(1/x)(2x - 1/x)

⇒  512 = 8x3 - 1/x3 - 6(8)

⇒ 8x3 - 1/x3 = 512 + 48

⇒ 560