This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

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Found problems: 2

2018 Middle European Mathematical Olympiad, 1
Tags: inequalities , am-gm inequality , easy problem
Let $a,b$ and $c$ be positive real numbers satisfying $abc=1.$ Prove that$$\frac{a^2-b^2}{a+bc}+\frac{b^2-c^2}{b+ca}+\frac{c^2-a^2}{c+ab}\leq a+b+c-3.$$

2002 Canada National Olympiad, 3
Tags: inequalities , Canada , AM-GM , am-gm inequality , algebra
Prove that for all positive real numbers $a$, $b$, and $c$, \[ \frac{a^3}{bc} + \frac{b^3}{ca} + \frac{c^3}{ab} \geq a+b+c \] and determine when equality occurs.