Assume roots (α,β) = (2,2) because Product of roots α*β = 2*2 = 4 is satisfying as per question.
Let n=3
(α^n+β^n)/(α^−n+β^−n) = (2^3+2^3)/(2^-3+2^-3) = (8+8)/(1/8)+(1/8) = 16/(1/4) = 16*4 = 64
Now trying option elimination with n=3
Option B = 4^n = 4^4= 64
Matching with our answer 64 which was calculated above