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Inequality with a parameter

Source: 2007 Bulgarian Autumn Math Competition, Problem 11.2

March 17, 2022
inequalitiesparameteralgebra

Problem Statement

Find all values of the parameter aa for which the inequality x−x2−a+6a−2x−x2≤10a−2x−4x2\sqrt{x-x^2-a}+\sqrt{6a-2x-x^2}\leq \sqrt{10a-2x-4x^2} has a unique solution.
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