若x/3=y/2=z/5,则分式xy+yz+zx/x²+y²+z²等于?_数学解答

若x/3=y/2=z/5,则分式xy+yz+zx/x²+y²+z²等于?

人气：150 ℃　时间：2020-04-06 04:18:37

解答

设x/3=y/2=z/5=k
则x=3k,y=2k,z=5k
xy+xz+yz/x^2+y^2+z^2
=(6k^2+15k^2+10k^2)/(9k^2+4k^2+25k^2)
=(6+15+10)/(9+4+25)
=31/38