已知x/2=y/3=z/4求(Xy+yz+zx)/(x^2+y^2+z^2)

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已知x/2=y/3=z/4求(Xy+yz+zx)/(x^2+y^2+z^2)
已知x/2=y/3=z/4求(Xy+yz+zx)/(x^2+y^2+z^2)

已知x/2=y/3=z/4求(Xy+yz+zx)/(x^2+y^2+z^2)
设x/2=y/3=z/4=k
则x=2k,y=3k,z=4k
(xy+yz+zx)/(x^2+y^2+z^2)=(6k^2+12k^2+8k^2)/(4k^2+9k^2+16k^2)=26/29