#roots-of-unity

solving $x^{2026}+\frac{1}{x^{2026}}$ given $x+\frac{1}{x}=1$

Question > if $x+\frac{1}{x}=1$, solve $x^{2026}+\frac{1}{x^{2026}}=$ ? --- Answer From $x+\frac1x=1$, multiply through by $x$ (note $x\neq 0$):…