If x - \frac{1}{x} = 2, x > 0; then what is x^2 - \frac{1}{x^2} equal to?

Explanation

We know (x + \frac{1}{x})^2 = (x - \frac{1}{x})^2 + 4 = 2^2 + 4 = 8. Thus, x + \frac{1}{x} = \sqrt{8} = 2\sqrt{2} (since x > 0). Then, x^2 - \frac{1}{x^2} = (x - \frac{1}{x})(x + \frac{1}{x}) = 2 \times 2\sqrt{2} = 4\sqrt{2}.

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