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China South East Mathematical Olympiad 2013 Q1

Source: 27 Jul 2013

July 30, 2013

inequalitiesalgebracubic functionroots

Problem Statement

Let

a,b

be real numbers such that the equation

x^3-ax^2+bx-a=0

has three positive real roots . Find the minimum of

\frac{2a^3-3ab+3a}{b+1}