因为x^2-3x+1=0
所以x^2=3x-1
所以x^2+1/x^2
=(3x-1)+1/(3x-1)
=[(3x-1)^2+1]/(3x-1)
=(9x^2-6x+2)/(3x-1)
=[9(3x-1)-2(3x-1)]/(3x-1)
=7(3x-1)/(3x-1)
=7