A Two-Variable Exponential Domination

Problem

Suppose

4ax \leqslant e^{x+y-2} + e^{x-y-2} + 2 \qquad \text{for all } x, y \in [0, +\infty).

Find the maximum value of the real number $a$ .

Answer

Solution

Difficulty	8/10
Topics	Extrema, calculus, AM-GM, inequality

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