Question

if x-1/x=4 find x4-1/x4

Answer 1

$$\begin{gathered} \mathrm{x}-\frac{1}{\mathrm{x}}=4 \\ \mathrm{Squaring}\mathrm{we}\mathrm{get}, \\ {\mathrm{x}}^2+\frac{1}{{\mathrm{x}}^2}+2=16 \\ {\mathrm{x}}^2+\frac{1}{{\mathrm{x}}^2}=14 \\ \mathrm{Again}\mathrm{squaring}\mathrm{we}\mathrm{get}, \\ {\mathrm{x}}^4+\frac{1}{{\mathrm{x}}^4}+2=196 \\ {\mathrm{x}}^4+\frac{1}{{\mathrm{x}}^4}=194 \\ \mathrm{Now}, \\ \left({\mathrm{x}}^4-\frac{1}{{\mathrm{x}}^4}\right)=\sqrt{{\left({\mathrm{x}}^4+\frac{1}{{\mathrm{x}}^4}\right)}^2-4}=\sqrt{{194}^2-4} \end{gathered}$$