Related concept for this equation?

One friend of mine has a cup with a lot of equations and the other day I saw it and I do not know what equation is.

Which is the history behind this equation and what is the related concept?

Thanks

• Wikipedia calls it "inequality of arithmetic and geometric means", it was known before even Euclid. The tradition ascribes the discovery (along with the harmonic mean) to Pythagoreans. – Conifold Mar 7 '17 at 21:56
• That last part needs care when written. Write $\frac{a+b}{2}$ or $(a+b)/2$ so it is clear that it is not $a+(b/2)$. – Gerald Edgar Mar 8 '17 at 1:06
• @GeraldEdgar This is an answer! Post and I vote you up. On the other hand, thanks for your answer. – Maik Mar 9 '17 at 7:38