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

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Found problems: 2

1994 Irish Math Olympiad, 1
Tags: quadratic , ireland , integration , algebra , calculus , number theory
Let $ x,y$ be positive integers with $ y>3$ and $ x^2\plus{}y^4\equal{}2((x\minus{}6)^2\plus{}(y\plus{}1)^2).$ Prove that: $ x^2\plus{}y^4\equal{}1994.$

2000 Irish Math Olympiad, 1
Tags: ireland , inequalities , algebra
Prove that if $ x,y$ are nonnegative real numbers with $ x\plus{}y\equal{}2$, then: $ x^2 y^2 (x^2\plus{}y^2) \le 2$.