x^2-3x+1=0
x-3+(1/x)=0
x+(1/x)=3
x^3+(1/x)^3
=[x+(1/x)][x^2-x+(1/x)^2]
=3*(7-x)
=21-3x
x^4+(1/x)^4
=[x^2+(1/x^2)]^2-2
={[x+(1/x)]^2-2}^2-2
=(3^2-2)^2-2
=47