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Minimize (a+5)^2+(b-2)^2+(c-9)^2 subject to a constraint

Source: Turkey JBMO TST 2014 P4

June 21, 2014
inequalities proposedinequalities

Problem Statement

Determine the smallest value of (a+5)2+(b−2)2+(c−9)2(a+5)^2+(b-2)^2+(c-9)^2 for all real numbers a,b,ca, b, c satisfying a2+b2+c2−ab−bc−ca=3a^2+b^2+c^2-ab-bc-ca=3.
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