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求最小值已知x,y,z∈R+且满足xyz(x+y+z)=1,则(

2008-03-08 09:26:23江***
已知x,y,z∈R+且满足xyz(x+y+z)=1,则(x+y)(y+z)的最小值为________.求最小值已知x,y,z∈R+且满足xyz(x+y+z)=1,则(x+y)(y+z)的最小值为________.：已知x,y,z∈R+且满足xyz(x+y+z)=?

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  • 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
    2008-03-08 10:11:07
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