x/3=y/2=z/5,(xy+yz+zx)/(x²+y²+z²)=

问题描述:

x/3=y/2=z/5,(xy+yz+zx)/(x²+y²+z²)=

设x/3=y/2=z/5=k
则x=3k,y=2k,z=5k
∴,(xy+yz+zx)/(x²+y²+z²)=(6k²+10k²+15k²)/(9k²+4k²+25k²)=31/38