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min of a+b+c+ {3/(ab+bc+ca) if a,b,c>0 with a^2+b^2+c^2=1

Source: Mathcenter Contest / Oly - Thai Forum 2012 (R1) p2 sl-9 https://artofproblemsolving.com/community/c3196914_mathcenter_contest

November 13, 2022
algebrainequalities

Problem Statement

Let a,b,c∈R+a,b,c \in \mathbb{R}^+ where a2+b2+c2=1a^2+b^2+c^2=1. Find the minimum value of . a+b+c+3ab+bc+caa+b+c+\frac{3}{ab+bc+ca} (PP-nine)
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