MathDB
Minimum and maximum

Source: 2019 MEMO Problem T-1

August 30, 2019
algebrainequalitiesmemoMEMO 2019

Problem Statement

Determine the smallest and the greatest possible values of the expression (1a2+1+1b2+1+1c2+1)(a2a2+1+b2b2+1+c2c2+1)\left( \frac{1}{a^2+1}+\frac{1}{b^2+1}+\frac{1}{c^2+1}\right)\left( \frac{a^2}{a^2+1}+\frac{b^2}{b^2+1}+\frac{c^2}{c^2+1}\right) provided a,ba,b and cc are non-negative real numbers satisfying ab+bc+ca=1ab+bc+ca=1.
Proposed by Walther Janous, Austria
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