Let $a,b,c$ be positive real numbers such that $a+b+c=10$ and $ab+bc+ca=25$.  Let $m=\min\{ab,bc,ca\}$.  Find the largest possible value of $m$.
Question:
Let $a,b,c$ be positive real numbers such that $a+b+c=10$ and $ab+bc+ca=25$.  Let $m=\min\{ab,bc,ca\}$.  Find the largest possible value of $m$.
Answer:
Let's think step by step.

user
\frac{25}{9}
Let $a,b,c$ be positive real numbers such that $a+b+c=10$ and $ab+bc+ca=25$.  Let $m=\min\{ab,bc,ca\}$.  Find the largest possible value of $m$.
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