If $ x - \frac{1}{x}= 11$ and x > 0, what is the value of $ (x^2 -\frac{1}{x^2})$ ?

$55\sqrt{5}$

If $ x - \frac{1}{x}= 11$ and x > 0,

what is the value of $ (x^2 -\frac{1}{x^2})$

If x - \(\frac{1}{x}\)  = n

then, x + \(\frac{1}{x}\)  = \(\sqrt {n^2 + 4}\)

We also know that,

a² - b² = (a + b) (a – b)

If $ x - \frac{1}{x}= 11$ 

then, x + \(\frac{1}{x}\)  = \(\sqrt {11^2 + 4}\) = 5\(\sqrt {5}\)

The value of $ (x^2 -\frac{1}{x^2})$ = 5\(\sqrt {5}\) × 11 = $55\sqrt{5}$