Question

if x+1/x=-2 then x2017+1/x2017=?​

Answer 1

has no solution

x+1x+2=0

is the same as

x2+2x+1=0

for x≠0 but is not a solution any way

x2+2x+1=(x+1)2

So we can conclude that x=−1

Now (−1)n={−11n is oddn is even

So (−1)2016+1(−1)2017=1+(−1)=0