(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

prove 2ab<= a^2+b^2 using order axioms

Of course use of other basic axioms for real numbers are also okay.

2. Relevant equations

axioms for set of real numbers.

3. The attempt at a solution

The easy way to do this would be just subtract 2ab from both sides, factor, and see that (a-b)^2 is greater or equal to zero.

But we have to use the basic axioms. So I tried constructing a^2+b^2-2ab by multiplying (a-b)(a-b) using the axioms. I'm not sure I was rigorous enough. Also I'm not sure whether I can just say a square of a real number is greater than zero. Though it is easy to prove.

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# Homework Help: Prove 2ab<= a^2+b^2 using order axioms

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