Can anyone prove the following inequality:

where , and is a real quantity (can be both negative or positive)?

It appears that the inequality is valid (even used random numbers), but can't see how to prove it.

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- Jun 6th 2007, 10:04 AMpuch7524Prove an inequality
Can anyone prove the following inequality:

where , and is a real quantity (can be both negative or positive)?

It appears that the inequality is valid (even used random numbers), but can't see how to prove it. - Jun 6th 2007, 11:56 AMThePerfectHacker
This inequality gets really messy really quickly. So I will prove the special case . I am sure you can use the same method to generalize it to more terms but it just is so messy.

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First, I think you meant .

Thus, we have to show:

Rewrite as,

Multiply by :

Open and cancel,

This is the AM-GM inequality.

Which is true.

(Or you can write ).