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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?

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Thanks

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    $\begingroup$ 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. $\endgroup$ – Conifold Mar 7 '17 at 21:56
  • $\begingroup$ That last part needs care when written. Write $\frac{a+b}{2}$ or $(a+b)/2$ so it is clear that it is not $a+(b/2)$. $\endgroup$ – Gerald Edgar Mar 8 '17 at 1:06
  • $\begingroup$ @GeraldEdgar This is an answer! Post and I vote you up. On the other hand, thanks for your answer. $\endgroup$ – Maik Mar 9 '17 at 7:38
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The formula √(ab) ≤ (a+b)/2 manifest an upper limit of the √(ab). If I square both therms I obtain ab ≤ ab + (a^2+b^2)/2 It's obvoius that ab is less than ab + (a^2+b^2)/2 The inequality a^2 < 2*a^2 holds for a=b
The inequality 1 < 2 holds for a=b=1 etc.
The equality holds trivially for a=b=0

Hope its ok ....

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    $\begingroup$ He asked for the history behind the equation. $\endgroup$ – Gerald Edgar Apr 6 '17 at 19:35

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