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Inequality with condition abc+a+b+c=ab+bc+ca+5

Source: 2020 Caucasus Mathematical Olympiad

March 16, 2020
inequalitiesalgebraHigh school olympiad

Problem Statement

Let real aa, bb, and cc satisfy abc+a+b+c=ab+bc+ca+5.abc+a+b+c=ab+bc+ca+5. Find the least possible value of a2+b2+c2a^2+b^2+c^2.
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