令(y+z)/x＝(z+x)/y＝(x+y)z＝k
则:1式:y+z＝kx
2式:z+x＝ky
3式:x+y＝kz
1式+2式+3式得:2(x+y+z)＝k(x+y+z)
∵xyz≠0,∴x,y,z均不为0
由此得:k＝2
(z+y)(x+z)(y+z)/[xyz]=[y+z)/x]×[(z+x)/y]×[(x+y)z]=k×k×k=2×2×2
=8