已知x/2=y/3=z/4求(Xy+yz+zx)/(5x^2+3y^2+z^2)的值

已知x/2=y/3=z/4求(Xy+yz+zx)/(5x^2+3y^2+z^2)的值
已知x/2=y/3=z/4求(Xy+yz+zx)/(5x^2+3y^2+z^2)的值

已知x/2=y/3=z/4求(Xy+yz+zx)/(5x^2+3y^2+z^2)的值
已知x/2=y/3=z/4求(Xy+yz+zx)/(5x^2+3y^2+z^2)的值
设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*4k^2+3*9k^2+16k^2)
=(6+12+8)/(20+27+16)
=26/63