若x^2-13x+1=0,则x^4+1/x^4的个位数是几

Question

若x^2-13x+1=0,则x^4+1/x^4的个位数是几

Answer 1

x^2-13x+1=0
x^2+1=13x
x+1/x=13
(x+1/x)^2=x^2+1/x^2+2=169
x^2+1/x^2=169-2=167
(x^2+1/x^2)^2=x^4+1/x^4+2=2789
x^4+1/x^4=27889-2=27887
x^4+1/x^4的个位数是7