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VN TST 1996 Question 3

VMO · VN TST 1996

Question 3

For real numbers $a,b,c$, find the minimum of $F(a,b,c)=(a+b)^4+(b+c)^4+(c+a)^4-\tfrac47(a^4+b^4+c^4)$.

The supplied source has no question point values. Each problem uses 1 editorial point for import compatibility; this is not an official scoring scale.