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

A. \(30\sqrt{3}\)

B. \(18\sqrt{3}\)

C. \(24\sqrt{3}\)

D. \(12\sqrt{3}\)

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

1 answer

Best answer

Answer: B. \(18\sqrt{3}\)

Answer: (B) \(18\sqrt{3}\)

\(\frac{1}{x} = \sqrt{3} - \sqrt{2}\), so \(x + \frac{1}{x} = 2\sqrt{3}\).

\(x^3 + \frac{1}{x^3} = (2\sqrt{3})^3 - 3(2\sqrt{3}) = 24\sqrt{3} - 6\sqrt{3} = 18\sqrt{3}\).

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

Was this answer helpful?