设x,y,z为正数,且xyz(x+y+z)=4,则(x+y)(y+z)的最小值
问题描述:
设x,y,z为正数,且xyz(x+y+z)=4,则(x+y)(y+z)的最小值
答
(x+y)(y+z)=xy+y^2+xz+yz=y(x+y+z)+xz ≥ 2√(x+y+z)xyz=4
设x,y,z为正数,且xyz(x+y+z)=4,则(x+y)(y+z)的最小值
(x+y)(y+z)=xy+y^2+xz+yz=y(x+y+z)+xz ≥ 2√(x+y+z)xyz=4