x/3=y/2=z/5,求xy+yz+xz/x²+y²+z²

问题描述:

x/3=y/2=z/5,求xy+yz+xz/x²+y²+z²

令 x/3=y/2=z/5=k
则 x=3k y=2k z=5k
∴(xy+yz+zx)/(x²+y²+z²)
=(6+10+15)k²/(9+4+25)l²
=31/38