\(x^2 - 3x + 1 = 0\) হলে \(\left(x^2 - \frac{1}{x^2}\right)\) এর মান -

\(x^2 - 3x + 1 = 0\) থেকে \(x + \frac{1}{x} = 3\)।

\(\left(x - \frac{1}{x}\right)^2 = \left(x + \frac{1}{x}\right)^2 - 4 = 9 - 4 = 5\), তাই \(x - \frac{1}{x} = \sqrt{5}\)।

\(x^2 - \frac{1}{x^2} = \left(x + \frac{1}{x}\right)\left(x - \frac{1}{x}\right) = 3\sqrt{5}\)