Exams › SSC CGL (Prelims) › General

Given \(\sqrt{x+5}+\sqrt{x}=5\), find the value of \(x\).

1. 1
2. 9
3. 4
4. 16

Correct answer: 4

Solution

Let \(\sqrt{x}=t\). Then \(\sqrt{t^2+5}+t=5\), so \(\sqrt{t^2+5}=5-t\). Squaring gives \(t^2+5=25-10t+t^2\), hence \(t=2\) and \(x=4\).

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