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 September 11th, 2018, 10:48 PM #1 Senior Member   Joined: May 2015 From: Arlington, VA Posts: 397 Thanks: 27 Math Focus: Number theory Equality of averages Given x not equal to y, when does their arithmetic average equal their geometric average?
 September 11th, 2018, 11:37 PM #2 Global Moderator   Joined: Dec 2006 Posts: 20,373 Thanks: 2010 What makes you think that's possible?
September 12th, 2018, 04:51 AM   #3
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Quote:
 Originally Posted by Loren Given x not equal to y, when does their arithmetic average equal their geometric average?
Never. This is the AM/GM inequality. It says GM $\leq$ AM with equality if and only if $x=y$.

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