x^2-3x+1=0
x-3+1/x=0
x+1/x=3
(x+1/x)^2=9
x^2+2+1/x^2=9
x^2+1/x^2=7
(x^2+1/x^2)^2=49
x^4+2+1/x^4=49
x^4+1/x^4=47