已知2/x=3/y=4/z,求4x^2+2yz+z^2/x+y+z*x-z-y/8x^2+4yz+2z^2的值

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已知2/x=3/y=4/z,求4x^2+2yz+z^2/x+y+z*x-z-y/8x^2+4yz+2z^2的值
已知2/x=3/y=4/z,求4x^2+2yz+z^2/x+y+z*x-z-y/8x^2+4yz+2z^2的值

已知2/x=3/y=4/z,求4x^2+2yz+z^2/x+y+z*x-z-y/8x^2+4yz+2z^2的值
两种方法：
1、一般法
设2/x=3/y=4/z=1/k,则x=2k,y=3k,z=4k,于是
4x^2+2yz+z^2/x+y+z*x-z-y/8x^2+4yz+2z^2
=[4(2k)^2+2*3k*4k+(4k)^2]/(2k+3k+4k) * (2k-4k-3k)/[8(2k)^2+4*3k*4k+2(4k)^2]
=(56k^2)/(9k) * (-5k)/[(112k^2)
=56k/9*(-5/112k)
=-5/18
2、特殊值法：令x=2,y=3,z=4代入上式可求（略）.
方法3：先化简,再求值
4x^2+2yz+z^2/x+y+z*x-z-y/8x^2+4yz+2z^2
=4x^2+2yz+z^2/x+y+z*x-z-y/2(4x^2+2yz+z^2)
=(x-z-y)/2(x+y+z)
=-5/18

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