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SSC CPO 2025 PYQ — Question 104

SSC CPO - 9 Dec 2025 - Shift 2 • Quantitative Aptitude • Q104

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If x+1x=2x + \frac{1}{x} = 2 , find the value of x6+1x6−3(x3+1x3)+5(x2+1x2)x^6 + \frac{1}{x^6} - 3\left(x^3 + \frac{1}{x^3}\right) + 5\left(x^2 + \frac{1}{x^2}\right) .

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Correct answer: C

Explanation

x+1x=2⇒x=1x=1⇒1x=1x6+1x6=1+1=2x3+1x3=1+1=2x2+1x2=1+1=2x6+1x6−3(x3+1x3)+5(x2+1x2)=2−3×2+5×2=2−6+10=6 x + \frac{1}{x} = 2 \Rightarrow x = 1\\ x = 1 \Rightarrow \frac{1}{x} = 1\\ x^6 + \frac{1}{x^6} = 1 + 1 = 2\\ x^3 + \frac{1}{x^3} = 1 + 1 = 2\\ x^2 + \frac{1}{x^2} = 1 + 1 = 2\\ x^6 + \frac{1}{x^6} - 3\left(x^3 + \frac{1}{x^3}\right) + 5\left(x^2 + \frac{1}{x^2}\right)\\ = 2 - 3 \times 2 + 5 \times 2\\ = 2 - 6 + 10\\ = 6