x/3=y/4=z/5 求xy+yz+zx/x^2+y^2+z^2的值

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x/3=y/4=z/5 求xy+yz+zx/x^2+y^2+z^2的值
x/3=y/4=z/5 求xy+yz+zx/x^2+y^2+z^2的值

x/3=y/4=z/5 求xy+yz+zx/x^2+y^2+z^2的值
x/3=y/4=z/5=k
x=3k,y=4k,z=5k
xy+yz+zx/x^2+y^2+z^2
=12k^2+20k^2+15k^2/9k^2+16k^2+25k^2
47/50

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