題目應(yīng)該是：x/(x^2-x-1)=7,求：x^2/(x^4+x^2+1)=?
由題知,x≠0,所以已知兩邊同時(shí)取倒數(shù),得
(x^2-x-1)/x=1/7
x-1-/x=1/7
x-1/x=8/7
上式兩邊同時(shí)平方,得
x^2+1/x^2-2=64/49
x^2+1/x^2=162/49
先算
(x^4+x^2+1)/x^2
=x^2+1/x^2+1
=162/49+1
=211/49
所以
x^2/(x^4+x^2+1)=49/211