\(x = \sqrt{4} + \sqrt{3}\) হলে, \(x^3 + \frac{1}{x^3}\) এর মান কত?

\(\frac{1}{x} = \frac{1}{\sqrt{4}+\sqrt{3}} = \frac{\sqrt{4}-\sqrt{3}}{(\sqrt{4})^2-(\sqrt{3})^2} = \sqrt{4}-\sqrt{3}\)

\(x + \frac{1}{x} = 2\sqrt{4} = 2 \times 2 = 4\)

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

\(= 4^3 - 3 \times 4 = 64 - 12 = 52\)