Maximum of Minimum

Author: mathforces
Problem has been solved: 21 times

Русский язык | English Language

Let $x$, $y$ and $z$ be positive numbers for which $x + y + z = 10$ and $xy + yz + zx = 25$. Let the irreducible fraction $\frac{m}{n}$ be the largest possible value of the minimum of the numbers $xy$, $yz$ and $zx$. What is $m^2n^2$?