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SSC CGL 2021 PYQ — Question 61

SSC CGL - 13 Aug 2021 - Shift 2 • Quantitative Aptitude • Q61

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If x - 1x\frac{1}{x}=5, x ≠ 0, then what is the value of x6−5x3−1x6+7x3−1 \frac{x^6 - 5x^3 - 1}{x^6 + 7x^3 - 1}?

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 4549\frac{45}{49}

x6−5x3−1x6+7x3−1 \frac{x^6 - 5x^3 - 1}{x^6 + 7x^3 - 1}

⇒ (x3 - 5 - 1/x3) / (x3 +7 - 1/x3)     [Divide both numerator and denominator by x3]

⇒ {(x3 - 1/x3) -5} / {(x3 - 1/x3) + 7}

⇒ {(x - 1/x)3 + 3(x - 1/x) -5} / {(x - 1/x)3 + 3(x - 1/x) +7}

⇒ (53 + 3 × 5 -5) / (53 + 3 × 5 +7)

⇒ 45/49