已知x/x²-x+1=1/5,求x²/x四次方+x²+1的值
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已知x/x²-x+1=1/5,求x²/x四次方+x²+1的值
已知x/x²-x+1=1/5,求x²/x四次方+x²+1的值
已知x/x²-x+1=1/5,求x²/x四次方+x²+1的值
x/(x²-x+1)=1/5
两边取倒数
(x²-x+1)/x=5
x+1/x-1=5
x+1/x=6
那么(x^4+x²+1)/x²
=x²+1/x²+1
=(x+1/x)²-2+1
=6²-1=35
所以
x²/(x^4+x²+1)
=1/35
如仍有疑惑,欢迎追问.祝:
x/x²-x+1=1/5,
x²-6x+1=0
x+1/x=6
x²/x^4+x²+1=1/[(x²+1/x²)+1]=1/[(x+1/x)²-1]
=1/(36-1)
=1/35