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 \(\frac{m}{n}\) be the maximum value for which inequality holds and \(m,n\) are coprime integers. Compute \(m+n\).


Vietnam TST
Not an original problem when \(a,b,c,d\) appear.
This problem is in this Set.
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