Let's prove that if you want to maximise \(ab\) with \(a + b\) equal to a constant value \(k\), then you want \(a = b = \frac{k}{2}\).

Twitter proof

Twitter proof:
Take s = k/2. If a = s+h then b = s-h, from which we get that ab = (s+h)(s-h) = s^2 - h^2. Because we know h^2 >= 0, ab is maximised when h = 0, that is a = b = s = k/2.https://t.co/9ypegSMF2F

— Mathspp (@mathsppblog) November 5, 2020

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