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Regional Olympiad - FBH 2011 Grade 11 Problem 4

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2011

September 27, 2018

combinatoricsirrationalirrational number

Problem Statement

Prove that among any

6

irrational numbers you can pick three numbers

a

b

and

c

such that numbers

a+b

b+c

and

c+a

are irrational