若x+y+z不等于0,且x/(y+z)=y/(z+x)=z/(x+y),求x/(x+y+z)的值大神们帮帮忙

问题描述:

若x+y+z不等于0,且x/(y+z)=y/(z+x)=z/(x+y),求x/(x+y+z)的值大神们帮帮忙

x/(y+z)=y/(z+x)=z/(x+y), 所以(x+y+z)/(y+z+z+x+x+y)=x/(y+z) (x+y+z)/(2x+2y+2z)=x/(y+z) 1/2=x/(y+z) y+z=2xx/(x+y+z) =x/(x+2x) =1/3