Question

If $x=3-2\sqrt{2}$, then find the value of $(x^2-\frac{1}{x^2})$.

Answer 1

$x=3-2\sqrt{2}$,

$\frac{1}{x}=\frac{1}{3-2\sqrt{2}}\times \frac{3+2\sqrt{2}}{3+2\sqrt{2}}=3+2\sqrt{2}$

$x^2-\frac{1}{x^2}=(x+\frac{1}{x})(x-\frac{1}{x})=6\times (-4\sqrt{2})=-24\sqrt{2}$.