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x^2 + y^2 <= 2 => xy + 3 >= 2x + 2y

Source: Czech-Polish-Slovak Junior Match 2015, Individual p3 CPSJ

March 15, 2020
inequalitiesalgebra

Problem Statement

Real numbers x,yx, y satisfy the inequality x2+y2≤2x^2 + y^2 \le 2. Orove that xy+3≥2x+2yxy + 3 \ge 2x + 2y
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