已知x/2＝y/3=z/4,求xy+yz+zx/x^2+y^2+z^2的值

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

已知x/2＝y/3=z/4,求xy+yz+zx/x^2+y^2+z^2的值
令x/2＝y/3=z/4=a
则x=2a,y=3a,z=4a
代入,得
(xy+yz+zx)/(x^2+y^2+z^2)=(6a^2+12a^2+8a^2)/(4a^2+9a^2+16a^2)=26/29