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Positive symmetric expressions

Source: Czech and Slovak Olympiad 1959, National Round, Problem 2

June 14, 2024
inequalitiessymmetry

Problem Statement

Let a,b,ca, b, c be real numbers such that a+b+c>0a+b+c > 0, ab+bc+ca>0ab+bc+ca > 0, abc>0abc > 0. Show that a,b,ca, b, c are all positive.
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