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Part of 2015 Grand Duchy of Lithuania

Problems(1)

y^2 + y + \sqrt{y - x^2 -xy} <= 3xy

Source: 2015 Grand Duchy of Lithuania, Mathematical Contest p1 (Baltic Way TST)

10/3/2020
Find all pairs of real numbers (x,y)(x, y) for which the inequality y2+y+y−x2−xy≤3xyy^2 + y + \sqrt{y - x^2 -xy} \le 3xy holds.
inequalitiesalgebra