Question

Demonstre o resultado.

Answer 1

Olá, Marcelomachuca!

$\\\left (x +\frac{1}{x} \right )^2 = \left (-1 \right )^2\Rightarrow \boxed{x^2+\frac{1}{x^2}=-1}\\\\\\ \left (x^2+\frac{1}{x^2} \right )^2=\left (-1 \right )^2\Rightarrow \boxed{x^4+\frac{1}{x^4}=-1}\\\\\\ \left (x^4+\frac{1}{x^4} \right )^2=\left (-1 \right )^2 \Rightarrow \boxed{x^8+\frac{1}{x^8}=-1}\\\\\\\ \textrm{Logo,}\; \boxed{ \boxed{x^{1994}+\frac{1}{x^{1994}}=-1}}.$