Finally \(a=b=c\) fails

Algebra Level 4

Let \(a,b,c\) be positive reals such that \(a+b+c=10\) and \(ab+bc+ca=25\). Let \(m=\min(ab,bc,ca)\). Find the largest possible value of \(m\).

If the largest possible value of \(m\) is of the form \(\dfrac{m}{n}\) where m and n are coprime positive integers, enter your answer as \(m+n\).

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