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SSC CGL 2022 PYQ — Question 69

SSC CGL - 19 April 2022 - Shift 2 • Quantitative Aptitude • Q69

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If x2 - 5x - 1 = 0, what is the value ofx6−x4+x2−1x3\frac{x^6-x^4+x^2-1}{x^3}? 

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 135.

x2 - 5x - 1 = 0

Dividing both sides by x.

⇒ x - 5 - 1/x = 0

⇒ (x - 1/x) = p = 5  ....(1

x6−x4+x2−1x3\frac{x^6-x^4+x^2-1}{x^3}

⇒ x3 - x + (1/x) - (1/x3)

⇒ x3 - 1/x3 - (x - 1/x)

⇒ (x - 1/x)3 + 3(x - 1/x) - (x - 1/x)

⇒  p3 + 3p - p = 125 + 15 - 5 = 135