Question

若x^2-3x+1=0,求分式x^2/(x^4+x^2+1)的值

Answer 1

因为：x^2-3x+1=0,所以：x+1/x=3

所以：(x^4+x^2+1)/x^2=x^2+1+1/x^2=(x+1/x)^2-2+1=9-1=8

所以：x^2/(x^4+x^2+1)=1/8