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MathNet 2024-part-04 — 168 problems (EN–VI) Question 149

Math Olympiad Vault · MathNet 2024-part-04 — 168 problems (EN–VI)

Question 149

The irrational numbers $x, y$ are such that the numbers $x^2 + 2024y$, $y^2 + 2024x$ and $xy$ are rational. Find $x + y$.
Mihaela Berindeanu