已知x+1/x=3求x2/x4+x2+1的值

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已知x+1/x=3求x2/x4+x2+1的值
已知x+1/x=3求x2/x4+x2+1的值

已知x+1/x=3求x2/x4+x2+1的值
x2/x4+x2+1 上下除以x^2
=1/(x^2+1+1/x^2)
=1/[(x+1/x)^2-1]
=1/(9-1)
=1/8

（x^4+x^2+1)/x^2
=x²+1+1/x²
=(x+1/x)²-1
=3²-1
=8
∴x2/(x4+x2+1)=1/8

x2/x4+x2+1 分子分母同除以x2得
=1/(x^2+1+1/x^2)
=1/[(x+1/x)^2-1]
=1/(9-1)
=1/8

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