\(x = \sqrt{3} + \sqrt{2}\) হলে, \(x^3 + \frac{1}{x^3}\) এর মান কত?

\(\frac{1}{x} = \sqrt{3} - \sqrt{2}\), তাই \(x + \frac{1}{x} = 2\sqrt{3}\)।

\(x^3 + \frac{1}{x^3} = \left(x + \frac{1}{x}\right)^3 - 3\left(x + \frac{1}{x}\right)\)

\(= (2\sqrt{3})^3 - 3(2\sqrt{3}) = 24\sqrt{3} - 6\sqrt{3} = 18\sqrt{3}\)

মনে রাখুন: \(a^3 + \frac{1}{a^3} = \left(a + \frac{1}{a}\right)^3 - 3\left(a + \frac{1}{a}\right)\)