a,b,c > 0 a^3 b^3 + b^3 c^3 + c^3 a^3 ≥ a^4 bc + b^4 ac + c^4 ab How to proof the inequality?
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I would start by reducing each side. Do you have any other further information? i.e is a>b>c>0? or are a,b & c integers?
Originally Posted by AirRafer a,b,c > 0 a^3 b^3 + b^3 c^3 + c^3 a^3 ≥ a^4 bc + b^4 ac + c^4 ab How to proof the inequality? it's not always true. for example it doesn't hold for a = b = 1 and c = 2. my guess is that we need the condition
Oh,yes.it doesn't always true. There isn't a good way to proof it even the 0<a,b,c<1
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