a 2 ( a − b ) ( a − c ) b 2 c 2 + b 2 ( b − c ) ( b − a ) c 2 a 2 + c 2 ( c − a ) ( c − b ) a 2 b 2 > K
Find the greatest constant K upto three places of decimals such that the above inequality satisfies for all distinct positive real numbers a , b , c .
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