令 x/2=y/3=z/4=k
则,x=2k ,y=3k ,z=4k
(xy+yz+xz)/(x^2+y^2+z^2)
=(6k^2+12k^2+8k^2)/(4k^2+9k^2+16k^2)
=26k^2/29k^2
=26/29