已知x^2-3x+1=0,求分式x^2/x^4+3x^2+1的值要有过程

已知x^2-3x+1=0,求分式x^2/x^4+3x^2+1的值要有过程
已知x^2-3x+1=0,求分式x^2/x^4+3x^2+1的值
要有过程

已知x^2-3x+1=0,求分式x^2/x^4+3x^2+1的值要有过程
x^2-3x+1=0
x-3+1/x=0
x+1/x=3
(x+1/x)^2=9
x^2+1/x^2+2=9
x^2+1/x^2=7
x^2/x^4+3x^2+1
=1/(x^2+3+1/x^2)
=1/(7+3)
=1/10

化简分式：
= x^2 + 3/x + 1/x^2 = (x^2-3x+1) + (3/x)(1+x^2) + 1/x^2 - 1
= 9 + 1/x^2 - 1 =1/x^2 + 8
带入由x^2-3x+1=0 得到的x解