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sum 1/(a^2+1) >= 3/2 if ab+bc+ca = 3

Source: Mathcenter Contest / Oly - Thai Forum 2008 R3 p5 https://artofproblemsolving.com/community/c3196914_mathcenter_contest

November 9, 2022
algebrainequalities

Problem Statement

Let a,b,ca,b,c be positive real numbers where ab+bc+ca=3ab+bc+ca = 3. Prove that 1a2+1+1b2+1+1c2+1≥32.\dfrac{1}{a^2+1}+\dfrac{1}{b^2+1}+\dfrac{1}{c^2+1}\geq\dfrac{3} {2}. (dektep)
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