1a

Part of 2013 Abels Math Contest (Norwegian MO) Final

Problems(1)

if it is true that 3x^2 + y^2 >= -ax(x + y), find a

Source: Norwegian Mathematical Olympiad 2013 - Abel Competition p1a

Find all real numbers

a

such that the inequality

3x^2 + y^2 \ge -ax(x + y)

holds for all real numbers

x

y

inequalitiesalgebra