Question

If $x=3-2\sqrt{2}$, find the value of $x^4-\frac{1}{x^4}$

Answer 1

$Rationalising\frac{1}{x}$

$\frac{1}{x}=\frac{3+2\sqrt{2}}{(9-8)}=3+2\sqrt{2}$

$x^4-\frac{1}{x^4}={(17-12\sqrt{2})}^2-{(17+12\sqrt{2})}^2=0$