Problem 31

Algebra Level 5

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

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

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