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I'm going to use Lagrange multipliers (sorry, there's probably a much more elegant way)
Let
And Lagrange multipliers states that for some lambda,
So
And since
, the minimum is 3/2Last edited by Identity (2008-02-01 16:17:00)
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How do you know it is minimum and not maximum?
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It can't have a maximum because as a, b, and c go to infinity, so does the entire expression. That's the only way I can tell
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But
so they cant all go to infinity.
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Oh dear, you're right, I don't really know what then
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Hence the expression is not bounded above.
As for an alternative approach, how about starting with this:
Then just expand, rearrange, substitute for a+b+c and simplify.
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