/sci/ - Science & Math

So I'm doing my intro to proofs class and I thought I run something very easy by you guys. We were told to find something easy out and then prove it. I chose to show that when multiplying to numbers that add up to some amount, you get the largest number by having them equal each other. (e.g. let's take 6 for example, the largest number there is 3*3 = 9, as opposed to 2 * 4 = 8, or 1*5 = 5)

Here's my proof, I want to know if it qualifies as a proof.

Theorem:
Let N = a + b, where a, b > 0
then ab is the largest when a = b

Proof:
<div class="math">a^2 > ab</div> (To be proved)
where a != b
Let b < a
<div class="math">a^2 > ab</div>
<div class="math">a > b</div>
Q.E.D

The reason I'm worried and the reason I think this works is because I'm allowed to say "let b < a", right? It's just an arbitrary variable, so I can choose any of them to be greater or smaller right?

>>6819143
>using a shitty casio

I found your problem pleb