初二因式题目

x/(x^2+5x+1)=4

分子分母同时除以x

1/[x+(1/x)+5]=4

不难解出x+(1/x)=-19/4

x^2/(x^4-5x^2+1)

分子分母同时除以x^2

1/[x^2+(1/x^2)-5]

x^2+(1/x^2)=[x+(1/x)]^2-2=(-19/4)^2-2=329/16

1/[x^2+(1/x^2)-5]=1/[(329/16)-5]=16/249

所以x^2/(x^4-5x^2+1)的值为16/249

x^2/(x^4-5x^2+1)的值=4,
因为只要把所有项都乘个x就行，你试试吧！

x/(x^2 + 5x + 1)=4

1/(x + 1/x + 5) =4

(x + 1/x + 5)= 1/4

所以可以得到: x + 1/x = -19/4

则 x^2 + 1/x^2 = ( x + 1/x )^2 - 2 = 329/16

x^2/(x^4 - 5x^2 + 1) = 1/(x^2 + 1/x^2 - 5)

= 1/(329/16 - 5)

= 16/249

16/249