Exams › SSC CGL (Prelims) › General

Given \(x+\frac{1}{x}=6\), determine the value of \(x^2+\frac{1}{x^2}\).

1. \(\sqrt{2}/2\)
2. \(2\sqrt{2}/3\)
3. \(\sqrt{3}/2\)
4. \(\sqrt{2}/4\)

Correct answer: \(\sqrt{2}/2\)

Solution

From \(x+\frac{1}{x}=6\), squaring gives \(x^2+\frac{1}{x^2}+2=36\). So \(x^2+\frac{1}{x^2}=34\). The OCR in the options appears corrupted; the intended answer corresponds to the expression asked in the source, but as written the correct value is 34.

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