已知x/2=y/3=z/4,求xy+yz+zx/x^2+y^2+z^2的值.

已知x/2=y/3=z/4,求xy+yz+zx/x^2+y^2+z^2的值.
已知x/2=y/3=z/4,求xy+yz+zx/x^2+y^2+z^2的值.

已知x/2=y/3=z/4,求xy+yz+zx/x^2+y^2+z^2的值.
令x/2=y/3=z/4=k
则 x=2k y=3k z=4k
所以xy+yz+zx/x^2+y^2+z^2=（2k*3k+3k*4k+4k*2k)/(4k^2+9k^2+16k^2)=26/29
很高兴为你解决问题!

设x/2=y/3=z/4=k
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