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SSC CHSL 2025 PYQ — Question 70

SSC CHSL - 12 Nov 2025 - Shift 2 • Quantitative Aptitude • Q70

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Simplify: 15−2+15+2\frac{1}{\sqrt{5}-2} + \frac{1}{\sqrt{5}+2}

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Correct answer: A

Explanation

15−2+15+2=(5+2)+(5−2)(5−2)(5+2)=5+2+5−25−4=251=25\frac{1}{\sqrt{5}-2} + \frac{1}{\sqrt{5}+2}\\ = \frac{(\sqrt{5}+2) + (\sqrt{5}-2)}{(\sqrt{5}-2)(\sqrt{5}+2)}\\ = \frac{\sqrt{5}+2+\sqrt{5}-2}{5-4}\\ = \frac{2\sqrt{5}}{1}\\ = 2\sqrt{5}