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a,b,c of 6 irrational exists usch that a+b,b+c,c+a are irrationals

Source: Mathcenter Contest / Oly - Thai Forum 2008 R1 p5 https://artofproblemsolving.com/community/c3196914_mathcenter_contest

November 10, 2022
irrational numberalgebra

Problem Statement

There are 66 irrational numbers. Prove that there are always three of them, suppose a,b,ca,b,c such that a+ba+b,b+cb+c,c+ac+a are irrational numbers.
(Erken)
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