Over all reals
Over all triples of real numbers which satisfy , find the maximum value of the expression above.
The answer is 0.
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1 solution
Notice that
( a 2 + a b + b 2 ) 2 + ( a 3 b + b 3 c + c 3 a ) = ( a + b + c ) ( a 3 + 2 a 2 b + a b 2 + b 3 − a 2 c − a b c + a c 2 ) = 0
Implying that 2 0 1 6 ( a 3 b + b 3 c + c 3 a ) = − 2 0 1 6 ( a 2 + a b + b 2 ) 2 ≤ 0 ,
With equality if a = b = c = 0 .
Thus, the maximum is 0 .