Question

2y+z分之x = 2x+y分之z=2z+x分之y=k,则k=

Answer 1

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