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JBMO TST- Bosnia and Herzegovina 2022 P1

Source: JBMO TST 2022 Bosnia and Herzegovina P1

May 21, 2022
JBMO TSTalgebranational olympiad

Problem Statement

Let a,b,ca,b,c be real numbers such that a2−bc=b2−ca=c2−ab=2a^2-bc=b^2-ca=c^2-ab=2. Find the value of ab+bc+caab+bc+ca and find at least one triplet (a,b,c)(a,b,c) that satisfy those conditions.
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