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max \sqrt{b^2+c^2}/(3-a)+ \sqrt{c^2+a^2}/(3-b)+a+b-2022c if a^2+b^2+c^2=2

Source: 2022 Saudi Arabia JBMO TST 2.2

November 3, 2022
inequalitiesmaxalgebra

Problem Statement

Consider non-negative real numbers a,b,ca, b, c satisfying the condition a2+b2+c2=2a^2 + b^2 + c^2 = 2 . Find the maximum value of the following expression P=b2+c23−a+c2+a23−b+a+b−2022cP=\frac{\sqrt{b^2+c^2}}{3-a}+\frac{\sqrt{c^2+a^2}}{3-b}+a+b-2022c
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