An Odd-Looking Constraint

★ 7/10Substitution algebra Cauchy-Schwarz inequality

Problem

Positive reals $x, y$ satisfy

(2xy - 1)^2 = (5y + 2)(y - 2).

Find the maximum value of

x + \frac{1}{2y}.

Answer

Solution

Difficulty	7/10
Topics	Substitution, algebra, Cauchy-Schwarz, inequality

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