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SSC CGL 2025 PYQ — Question 40

SSC CGL - 20 Sep 2025 - Shift 1 • Quantitative Aptitude • Q40

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If x=2+3x=2+\sqrt3, find x−1xx-\frac{1}{x}

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Correct answer: B

Explanation

The correct answer is option 2 i.e. 232\sqrt{3}.

x = 2 + √3

⇒ 1x=12+3{1\over x}=\frac{1}{2+\sqrt3}

⇒ 1x=(2−3)(2+3)(2−3)=2−322−(3)2=2−34−3=2−3\frac{1}{x}=\frac{(2-\sqrt3)}{(2+\sqrt3)(2-\sqrt3)}=\frac{2-\sqrt3}{2^2-(\sqrt3)^2}=\frac{2-\sqrt3}{4-3}=2-\sqrt3

⇒ x – 1/x = (2 + √3) – (2 – √3) = 2 + √3 – 2 + √3 = 2√3