Problem 31

$a+b+c+d\geq \frac{m}{n}(ab+ac+ad+bc+bd+cd)$

Given that $a,b,c,d$ are non-negative and $2(ab+ac+ad+bc+bd+cd)+abc+abd+acd+bcd=16$ .Let $\frac{m}{n}$ be the maximum value for which inequality holds and $m,n$ are coprime integers. Compute $m+n$ .

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Vietnam TST

Not an original problem when $a,b,c,d$ appear.

This problem is in this Set .