The AM-GM Inequality

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There are many different and interesting inequalities in Math Olympiads. In this video, we will explore the AM-GM inequality, a basic yet essential tool for many problems. After being familiar with the AM-GM inequality, we will discover another inequality in the next video, the Power Mean inequality.

▼ Timestamps ▼
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00:00 - Background
00:30 - Getting Familiar
01:06 - Application
03:25 - Proof

  1. arcturus
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Комментарии
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great video.... understood nothing other than 1:53 gif of Gon

krishnasharmarollno.
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Great explanation! I haven't really gotten down how to convert inequalities into am gm form yet but still this is useful to know in case it is more obvious.

mnny
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Great video and great explanation! Thank you very much.

NatoSkato
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For what type of a, b, c the inequality problem shown in the video is valid? I feel a certain anxiety about possible negative values, that can't be used for the Cauchy's inequality ( aka AM-GM), will it be valid if some of the numbers are positive and others are negative ( obviously they easily add up to one in that case)

lukaskamin
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Are you planning to do other inequalities as well

gmncnr