设x/2=y/4=z/5=k不等于0
则：x=2k
y=4k
z=5k
将x,y,z代入：xy+yz+xz/x^2+y^2+z^2
=(2k*4k+2k*5k+4k*5k)/[(2k)^2+(4k)^2+(5k）^2]
=(8k^2+10k^2+20k^2)/(4k^2+16k^2+25k^2)
=38/45