已知x/2=y/3=z/4 求(2x^2-y^2+z^2)/(xy+2yz+3xz)

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已知x/2=y/3=z/4 求(2x^2-y^2+z^2)/(xy+2yz+3xz)
已知x/2=y/3=z/4 求(2x^2-y^2+z^2)/(xy+2yz+3xz)

已知x/2=y/3=z/4 求(2x^2-y^2+z^2)/(xy+2yz+3xz)
设x/2=y/3=z/4=k
x=2k,y=3k,z=4k
原式
(2x^2-y^2+z^2)/(xy+2yz+3xz)
=(8k^2-9k^2+16k^2)/(6k^2+24k^2+24k^2)
=(15k^2)/(54k^2)
=5/18
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