A Two-Form Domination

★ 7/10Quadratic Equations algebra AM-GM inequality Discriminant

Problem

Let $a, b$ be positive. If

x^2 + 2xy + 3y^2 \geqslant ax^2 + by^2 \qquad \text{for all } x, y \in \mathbb{R},

find the range of possible values of $a + b$ .

Answer

Solution

Difficulty	7/10
Topics	Quadratic Equations, algebra, AM-GM, inequality, Discriminant

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