5

Part of 1994 Chile National Olympiad

Problems(1)

x^{1994} +1/x^{1994} if x +1/x=-1 (Chile NMO 1994 P5)

Source:

x

be a number such that

x +\frac{1}{x}=-1

. Determine the value of

x^{1994} +\frac{1}{x^{1994}}