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MathNet 2019-part-05 — 184 problems (EN–VI) Question 48

Math Olympiad Vault · MathNet 2019-part-05 — 184 problems (EN–VI)

Question 48

Determine the numbers $x$, $y$, with $x$ integer and $y$ rational, for which the equality
$$
5(x^2 + xy + y^2) = 7(x + 2y)
$$
holds.