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

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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

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
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

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=2x x/(x+y+z) =x/(x+2x) =1/3

因为x/(y+z)=y/(z+x)=z/(x+y) 所以x/(y+z)+y/(z+x)+z/(x+y)=1/2=0.5 所以x/(y+z)=y/(z+x)=z/(x+y)=1/2=0.5 所以X=0.5(y+z) 将其代入x/(x+y+z),得 0.5(y+z)/0.5(y+z)+(y+z)=1/3 所以x/(x+y+z)=1/3