x^2-4x+1=0
x^2+1=4x
x+1/x=4
(x+1/x)^2=4^2
x^2+2+1/x^2=16
x^2+1/x^2=14
x^2-2+1/x^2=12
(x-1/x)^2=12
x-1/x=±√12
x-1/x=±2√3
x^2+1/x^2=14
(x^2+1/x^2)^=14^2
x^4+2+1/x^4=196
x^4+1/x^4=194