# 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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