已知x^2-5x+1=0,求x^2/(x^4+6x^2+1)的值.
问题描述：
已知x^2-5x+1=0,求x^2/(x^4+6x^2+1)的值.
答
x^2-5x+1=0
x-5+1/x=0 两边除以x
x+1/x=5
x²/(x^4+6x²+1)
=1/(x²+6+1/x²)
=1/[(x+1/x)²+4]
=1/29