A Symmetric Maximum on a Segment

★ 6/10Substitution algebra Completing the Square inequality Symmetry

Problem

Nonnegative reals $a, b$ satisfy $a + b = \dfrac{3}{2}$ . Find the maximum value of

a^2b^2 + \frac{9}{4}\left(a^2 + b^2\right).

Answer

Solution

Difficulty	6/10
Topics	Substitution, algebra, Completing the Square, inequality, Symmetry

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