x+1/x=4
两边平方得
x²+2+1/x²=16
两边减去1
x²+1+1/x²=15
左边通分
(x^4+x²+1)/x²=15
取倒数
x^2/(x^4+x^2+1)=1/15
因为(x^4+x^2+1)/x^2=x^2+1/x^2+1=(x+1/x)^2-1=16-1=15
所以x^2/(x^4+x^2+1)=1/15
x+1/x=4
(x+1/x)^2=4^2
x^2+2+1/x^2=16
x^2+1/x^2=14
x^2/(x^4+x^2+1)
=1/(x^2+1+1/x^2)
=1/(14+1)
=1/15
x+1/x=4
∴﹙x^4+x^2+1﹚／x²
=x²+1+1/x²
=x²+2+1/x²-1
=(x+1/x)²-1
=4²-1
=15
∴x^2/x^4+x^2+1=1/15
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