Ordering Three Constrained Reals

★ 7/10Substitution algebra AM-GM inequality

Problem

Let $a > 0$ , and suppose

a^2 - 2ab + c^2 = 0, \qquad bc > a^2.

Determine, with proof, the size order of $a, b, c$ .

Answer

Solution

Difficulty	7/10
Topics	Substitution, algebra, AM-GM, inequality

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