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Ineq - simple

Source: Indian RMO 2003 Problem 3

October 27, 2005
inequalities

Problem Statement

Let a,b,ca,b,c be three positive real numbers such that a+b+c=1a + b +c =1 . prove that among the three numbers a−ab,b−bc,c−caa-ab, b - bc, c-ca there is one which is at most 14\frac{1}{4} and there is one which is at least 29\frac{2}{9}.
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