যদি \(x^4 - x^2 + 1 = 0\) হয়, তবে \(x^3 + \frac{1}{x^3}\) = কত?

\(x^4 - x^2 + 1 = 0\) থেকে \(x^2 + \frac{1}{x^2} = 1\)।

তাই \(\left(x+\frac{1}{x}\right)^2 = 3\), অর্থাৎ \(x+\frac{1}{x} = \sqrt{3}\)।

\(x^3 + \frac{1}{x^3} = \left(x+\frac{1}{x}\right)^3 - 3\left(x+\frac{1}{x}\right) = 3\sqrt{3} - 3\sqrt{3} = 0\)

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