xyz=1 (1+x)(1+y)(1+z) - 2 >= 2*(((x/y)^(1/3)) * ((y/z)^(1/3)) * ((z/x)^(1/3)) ) How to proof it??

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Originally Posted by ferrumes xyz=1 (1+x)(1+y)(1+z) - 2 >= 2*(((x/y)^(1/3)) * ((y/z)^(1/3)) * ((z/x)^(1/3)) ) How to proof it?? What are the restrictions? must ?

Originally Posted by ferrumes xyz=1 (1+x)(1+y)(1+z) - 2 >= 2*(((x/y)^(1/3)) * ((y/z)^(1/3)) * ((z/x)^(1/3)) ) How to proof it?? Note that the 2nd side simplifies to 2, so all you have left is:

Originally Posted by Mathstud28 What are the restrictions? must ? yes [tex](x,y,z)\in\mathbb{Z}^{+}