An algebra problem by Victor Loh

Algebra Level 3

Given that \(a,b,c\) are positive reals such that the maximum value of \(N\) which satisfies the inequality

\[\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}\geq N\]

can be expressed in the form \(\frac{m}{n}\), where \(m\) and \(n\) are coprime, positive integers, find the value of \(m+n\).

\(\textbf{Details and Assumptions}\)

For those who know a certain inequality, this problem is going to be a no-brainer. :D


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