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SSC CGL 2020 PYQ — Question 71

SSC CGL Tier II - Quant - 16 Nov 2020 • Quantitative Aptitude • Q71

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If  x - 1x\frac{1}{x}= 5, x ≠ 0, then what is the value of x6+3x3−1x6−8x3−1\frac{x^6+3x^3-1}{x^6-8x^3-1}?

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Correct answer: B

Explanation

The correct answer is option 2 i.e. 1312\frac{13}{12}

 x - 1x\frac{1}{x}= 5.

On cubing both sides we get,

⇒ x3 - 1/x3 - 3(x - 1/x) = 125

⇒ x3 - 1/x3 = 140

x6+3x3−1x6−8x3−1\frac{x^6+3x^3-1}{x^6-8x^3-1},

On dividing the numerator and denominator by x3 we get,

= (x3 - 1/x3 + 3)/(x3 - 1/x3 - 8)

= (140 + 3)(140 - 8)

= 143/132

= 13/12.