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equation with no real solution

Source: JBMO 2007, Bulgaria, problem 1

June 28, 2007
quadraticsinequalitiesfunctionalgebraalgebra solvedinequalities solvedJBMO

Problem Statement

Let aa be positive real number such that a3=6(a+1)a^{3}=6(a+1). Prove that the equation x2+ax+a2āˆ’6=0x^{2}+ax+a^{2}-6=0 has no real solution.
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