TR-MO-R1 2013 Problem 11

$x^4 + y^4 + 2x^2y + 2xy^2 + 2 = x^2 + y^2 + 2x + 2y$ eşitliğini sağlayan kaç $(x, y)$ gerçel sayı ikilisi vardır?

a) 6 b) 5 c) 4 d) 3 e) 2

Official text Turkish Mathematical Olympiad, first round 2013 official paper, page 4. Quoted with source.

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