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September 11th, 2018, 11:48 PM   #1
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Equality of averages

Given x not equal to y, when does their arithmetic average equal their geometric average?
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September 12th, 2018, 12:37 AM   #2
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What makes you think that's possible?
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September 12th, 2018, 05:51 AM   #3
SDK
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Quote:
Originally Posted by Loren View Post
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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