2y+z分之x = 2x+y分之z=2z+x分之y=k,则k=

2y+z分之x = 2x+y分之z=2z+x分之y=k,则k=
2y+z分之x = 2x+y分之z=2z+x分之y=k,则k=

2y+z分之x = 2x+y分之z=2z+x分之y=k,则k=
x/(2y+z)=z/(2x+y)=y/(2z+x)=k
则
(2y+z)/x=(2x+y)/z=(2z+x)/y=1/k
根据何比定理
(2y+z)/x=(2x+y)/z=(2z+x)/y=（2y+z+2x+y+2z+x）/(x+y+z)=3
所以 1/k=3
k=1/3