A Necessary Probe

★ 7/10Quadratic Equations trigonometry Extrema Substitution inequality

Problem

The inequality

3\sin^2 x - \cos^2 x + 4a\cos x + a^2 \le 31

holds for all $x \in \mathbb{R}$ . Find the range of $a$ .

Answer

Solution

Difficulty	7/10
Topics	Quadratic Equations, trigonometry, Extrema, Substitution, inequality

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