=xy+xz+y^2+yz
=y(x+y+z)+xz
xyz(x+y+z)= 1
y(x+y+z)= 1/xz
xz & gt0， 1/xz & gt； 0
(x+y)(y+z)
= xz+ 1/xz & gt； =2√(xz* 1/xz)=2
The minimum value of (x+y) (y+z) is 2.