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SSC CGL 2025 PYQ — Question 73

SSC CGL - 17 Sep 2025 - Shift 1 • Quantitative Aptitude • Q73

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What is the value of 6+6+6+...\sqrt{6+\sqrt{6+\sqrt{6+...}}}?

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 3.

Let x=6+6+6+...x=\sqrt{6+\sqrt{6+\sqrt{6+...}}}

⇒ x=6+xx = \sqrt{6+x}

⇒ x2=6+xx^2 = 6+x

⇒ x2 - x - 6 = 0

⇒ (x - 3)(x + 2) = 0

⇒ x - 3 = 0

⇒ x = 3