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- Jun 15th 2008, 06:49 AM #1

- Joined
- Apr 2008
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- 48

- Jun 15th 2008, 06:58 AM #2

- Jun 15th 2008, 06:58 AM #3

- Jun 15th 2008, 07:00 AM #4
let be one of the numbers. so the other can be represented as

Let be the function representing the product as stated WLOG:

so, and we want the maximum, thus we need such that

therefore, either or but note that x is a positive number, therefore we take .

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optional: if , then we are sure that gives the maximum value for

and at , we have .