x+y+z=1／xyz 求（x+y）（y+z）的最小值
答案:1 mip版
解决时间 2021-08-02 20:20
- 提问者网友：莪早已看透了誓言
- 2021-08-01 21:50
x+y+z=1／xyz 求（x+y）（y+z）的最小值
最佳答案
- 二级知识专家网友：再见不见
- 2021-08-01 22:26
已知x,y,z∈R+且满足xyz(x+y+z)=1,则(x+y)(y+z)的最小值为____.
xyz(x+y+z)=1--->x+y+z=1/(xyz)
(x+y)(y+z)
= [1/(xyz)-z][1/(xyz)-x)]
= [1/(xyz)]² - [1/(yz)+1/(xy)] + xz
= (x+y+z)[1/(xyz)] - [1/(yz)+1/(xy)] + xz
= 1/(yz)+1/(xy)+1/(xz) - [1/yz-1/xy] + xz
= 1/(xz) + (xz)
≥ 2
--->xz=1时，(x+y)(y+z)的最小值为2
xyz(x+y+z)=1--->x+y+z=1/(xyz)
(x+y)(y+z)
= [1/(xyz)-z][1/(xyz)-x)]
= [1/(xyz)]² - [1/(yz)+1/(xy)] + xz
= (x+y+z)[1/(xyz)] - [1/(yz)+1/(xy)] + xz
= 1/(yz)+1/(xy)+1/(xz) - [1/yz-1/xy] + xz
= 1/(xz) + (xz)
≥ 2
--->xz=1时，(x+y)(y+z)的最小值为2
我要举报
如以上问答内容为低俗/色情/暴力/不良/侵权的信息，可以点下面链接进行举报，我们会做出相应处理，感谢你的支持！
点此我要举报以上问答信息
推荐资讯