Difference between revisions of "2017 USAMO Problems/Problem 6"

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given that <math>a,b,c,d,</math> are nonnegative real numbers such that <math>a+b+c+d=4</math>.
 
given that <math>a,b,c,d,</math> are nonnegative real numbers such that <math>a+b+c+d=4</math>.
  
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==Solution==
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See here: https://artofproblemsolving.com/community/c5t211539f5h1434574_looks_like_mount_inequality_erupted_
  
==Solution==
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or:
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https://www.youtube.com/watch?v=LSYP_KMbBNc

Latest revision as of 19:57, 26 December 2017

Problem

Find the minimum possible value of

\[\frac{a}{b^3+4}+\frac{b}{c^3+4}+\frac{c}{d^3+4}+\frac{d}{a^3+4},\]

given that $a,b,c,d,$ are nonnegative real numbers such that $a+b+c+d=4$.

Solution

See here: https://artofproblemsolving.com/community/c5t211539f5h1434574_looks_like_mount_inequality_erupted_

or:

https://www.youtube.com/watch?v=LSYP_KMbBNc