已知x/2=y/3=z/4,求xy+yz+zx/5x的方+3y的方+z的方

已知x/2=y/3=z/4,求xy+yz+zx/5x的方+3y的方+z的方
已知x/2=y/3=z/4,求xy+yz+zx/5x的方+3y的方+z的方

已知x/2=y/3=z/4,求xy+yz+zx/5x的方+3y的方+z的方
令x/2=y/3=z/4=k
x=2k
y=3k
z=4k
(xy+yz+zx)/(5x^2+3y^2+z^2)
=(2k*3k+3k*4k+4k*2k)/[5*(2k)^2+3*(3k)^2+(4k^2)]
=(6k^2+12k^2+8k^2)/(20k^2+27k^2+16k^2)
=26k^2/63k^2
=26/63

设x/2=y/3=z/4=k即可得结果哦26/63