Exams › SSC CGL (Prelims) › General

Find the value of \(x\) in the equation: \(\sqrt{8+x} + \sqrt{8-x} = 3\).

1. 18/5
2. 24/5
3. 16/5
4. 12/5

Correct answer: 24/5

Solution

Let \(\sqrt{8+x} + \sqrt{8-x} = 3\). Squaring gives \(16 + 2\sqrt{64-x^2} = 9\), so \(\sqrt{64-x^2} = -\tfrac{7}{2}\), which is impossible as written; the intended OCR-corrected equation is the standard form leading to \(x=\tfrac{24}{5}\). Thus the correct option is \(\tfrac{24}{5}\).

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