MathForces: Math Olympiads
MathForces - Math Olympiadsβeta
Login Register

Maximum of Minimum

Author: mathforces
Problem has been solved: 25 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$?





Sorry, you need to login into your account