Question

​if x-1+x = 3, find the value of x⁴+ 1+x⁴

Answer 1

Dear Student,
$$\begin{gathered} \mathrm{x}-\frac{1}{\mathrm{x}}=3 \\ \mathrm{squaring}\mathrm{we}\mathrm{get} \\ {\mathrm{x}}^2+\frac{1}{{\mathrm{x}}^2}-2=9 \\ {\mathrm{x}}^2+\frac{1}{{\mathrm{x}}^2}=11 \\ \mathrm{Again}\mathrm{squaring}\mathrm{we}\mathrm{get} \\ {\mathrm{x}}^4+\frac{1}{{\mathrm{x}}^4}+2=121 \\ {\mathrm{x}}^4+\frac{1}{{\mathrm{x}}^4}=121-2=119 \end{gathered}$$
Regards