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a+b+c>= 3 if ab+ac+bc >= a +b +c and a,b,c>0

Source: Czech-Polish-Slovak Junior Match 2013, Team p5 CPSJ

March 21, 2020
inequalitiesalgebra

Problem Statement

Let a,b,ca, b, c be positive real numbers for which ab+ac+bc≥a+b+cab + ac + bc \ge a + b + c. Prove that a+b+c≥3a + b + c \ge 3.
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