If \(x = 3 + 2\sqrt{2}\), what is the value of \(x^2 + \frac{1}{x^2}\)?

A. 32

B. 38

C. 36

D. 34

Doubtly AI Asked 27 Oct 2026 AI-generated · not yet verified ssc cgl Save WhatsApp Report

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Answer: D. 34

Answer: (D) 34

\(\frac{1}{x} = \frac{1}{3 + 2\sqrt{2}} = 3 - 2\sqrt{2}\) (multiply by the conjugate; 9 − 8 = 1).

So \(x + \frac{1}{x} = 6\) and \(x^2 + \frac{1}{x^2} = 36 - 2 = 34\).

Doubtly AI · 27 Oct 2026 AI-generated · not yet verified Report

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