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SSC CGL 2025 PYQ — Question 70

SSC CGL - 18 Sep 2025 - Shift 2 • Quantitative Aptitude • Q70

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Given, x+1x=4x + {1\over x} = 4 find the value of x6+1x6−3(x4+1x4)+4(x2+1x2)x^6 + {1\over x^6} - 3\left(x^4 + {1\over x^4}\right) + 4\left(x^2 + {1\over x^2}\right)

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Correct answer: A

Explanation

The correct answer is Option 1 i.e. 2176.

x+1x=4x + \frac{1}{x} = 4

x2+1x2=(x+1x)2−2=42−2=16−2=14x^2 + \frac{1}{x^2} =\left(x + \frac{1}{x}\right)^2 - 2 = 4^2 - 2 = 16 - 2 = 14

x4+1x4=(x2+1x2)−2=(14)2−2=196−2=194x^4 + \frac{1}{x^4} =\left(x^2 + \frac{1}{x^2} \right)-2= (14)^2 - 2 = 196 - 2 = 194

x6+1x6=(x2+1x2)3−3(x2+1x2)=143−3×14=2744−42=2702x^6 + \frac{1}{x^6} = (x^2 + \frac{1}{x^2})^3 - 3(x^2 + \frac{1}{x^2}) = 14^3 - 3 \times 14 = 2744 - 42 = 2702

x6+1x6−3(x4+1x4)+4(x2+1x2)x^6 + {1\over x^6} - 3\left(x^4 + {1\over x^4}\right) + 4\left(x^2 + {1\over x^2}\right) = 2702 - 3(194) + 4(14)

= 2702 - 582 + 56

= 2176