2014 USAJMO Problems

Day 1

Problem 1

Let $a$ , $b$ , $c$ be real numbers greater than or equal to $1$ . Prove that $\min{\left (\frac{10a^2-5a+1}{b^2-5b+1},\frac{10b^2-5b+1}{c^2-5c+10},\frac{10c^2-5c+1}{a^2-5a+10}\right )}\leq abc$ Solution

Problem 2

Solution

Problem 3

Solution

Day 2

Page

Toolbox

Search

2014 USAJMO Problems

Contents

Day 1

Problem 1

Problem 2

Problem 3

Day 2

Problem 4

Problem 5

Problem 6