A Simple Proof of the Arithmetic Mean Geometric Mean Inequality

Last February, we have used area to prove the Arithmetic Mean – Geometric Mean Inequality (AM-GM Inequality). In this post, we show a simpler proof.

 

Click image view the GeoGebra applet demonstration

Recall that the AM-GM Inequality states that given two numbers, their geometric mean is always less than or equal to their arithmetic mean.  That is given two numbers a and b,

\displaystyle\sqrt{ab} \leq \frac{a+b}{2} . » Read more

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