已知x/3=y/4=z/5,求xy+yz+zx/x²+y²+z²的值

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已知x/3=y/4=z/5,求xy+yz+zx/x²+y²+z²的值
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已知x/3=y/4=z/5,求xy+yz+zx/x²+y²+z²的值
已知x/3=y/4=z/5,求xy+yz+zx/x²+y²+z²的值

已知x/3=y/4=z/5,求xy+yz+zx/x²+y²+z²的值
令x/3=y/4=z/5=k
则x=3k,y=4k,z=5k
所以(xy+yz+zx)/(x^2+y^2+z^2)
=(12k²+20k²+15k²)/(9k²+16k²+25k²)
=47k²/50k²
=47/50