Question

If x+1/x=-1 then x^2016+1/x^2016=?

Answer 1

x+1/x = -1
x+1/x+1 =0
(x-1)(x+1/x+1) =0
(x^3)-1 =0
x^3 =1, x≠0

(x^2016)+(1/x^2016) =( x^(3*672))+(1/x^(3*672))
= (1^672) + (1/1^672)
= 1+1 =2.