Question

If x= 3 + 2 root 2,then the value of (x-1/x)³

Answer 1

$$\begin{gathered} \mathrm{x}-\frac{1}{\mathrm{x}}=3+2\sqrt{2}-\frac{1}{3+2\sqrt{2}} \\ =3+2\sqrt{2}-\frac{1}{3+2\sqrt{2}}\times \frac{3-2\sqrt{2}}{3-2\sqrt{2}} \\ =3+2\sqrt{2}-\frac{3-2\sqrt{2}}{9-8}=3+2\sqrt{2}-3+2\sqrt{2} \\ =4\sqrt{2} \\ {\left(\mathrm{x}-\frac{1}{\mathrm{x}}\right)}^3={\left(4\sqrt{2}\right)}^3=64\left(2\sqrt{2}\right)=128\sqrt{2}\mathrm{ANS}... \end{gathered}$$