Let .

Then

because .Let

.We find

(just). It follows that since the quadratic function is strictly increasing for positiveThe LHS is

and so we are done.]]>I missed that. I am sorry about that. Bob and I had a good discussion on that and it seems better to work backwards in that case. Even though they do work forwards a lot in inequality books.

Unfortunately, whatever brilliant idea I had about this problem 1 year ago, I can not remember it at all.

]]>I think what Agnishom wanted to ask you is whether it is okay to start the proof with what we want to prove and work our way to a true statement...

]]>This is the problem:

]]>Is it okay to start with the thing we are trying to prove?]]>

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