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min of ab/c+bc/a+ca/b when a,b,c>0 with a^2 + b^2 + c^2 = 1

Source: Germany Federal - Bundeswettbewerb Mathematik 2019 round 2, p2

April 16, 2020
inequalitiesminalgebra

Problem Statement

Determine the smallest possible value of the sum S(a,b,c)=abc+bca+cabS (a, b, c) = \frac{ab}{c}+\frac{bc}{a}+\frac{ca}{b} where a,b,ca, b, c are three positive real numbers with a2+b2+c2=1a^2 + b^2 + c^2 = 1
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