If x - \(\frac{1}{x}\) = 2\(\sqrt{2}\)

then find the value of  x² - \(\frac{1}{x^2}\).

4\(\sqrt{3}\)

⇒ If x - \(\frac{1}{x}\) = a then x + \(\frac{1}{x}\) = \(\sqrt {a^2 + 4}\)

Here,

x - \(\frac{1}{x}\) =2\(\sqrt{2}\), then 

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

Formula → x² - y² = (x + y) (x - y)

⇒ x² - \(\frac{1}{x^2}\) = (x + \(\frac{1}{x}\)) (x - \(\frac{1}{x}\))

                = 2\(\sqrt {3}\) × 2\(\sqrt{2}\)

                = 4\(\sqrt{6}\)