Question

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

Answer 1

$x=2-\sqrt{3}$

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

$=\frac{2+\sqrt{3}}{4-3}=\frac{2+\sqrt{3}}{1}$

${\left(x-\frac{1}{x}\right)}^3={\left(2-\sqrt{3}-2-\sqrt{3}\right)}^3=24\sqrt{3}$