TR-MO-R1 2023 Problem 31

$(xy+2)^2+10(x+y)+21=2(x^3+y^3)+5(x^2+y^2)$

eşitliğini sağlayan $x$ ve $y$ gerçel sayıları için, $x^2+y^2$ en az kaçtır?

a) $2$ b) $3$ c) $4$ d) $5$ e) Hiçbiri

Dataset text TÜBİTAK olympiad set, Matematik_2023_1.Asama_31. Quoted with source.

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