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2023 Polish Junior Math Olympiad Round 1 P5

Source:

May 21, 2023
inequalitiesalgebra

Problem Statement

Positive numbers aa, bb, cc satisfy the inequalities a + b \geq ab,   b + c \geq bc, \text{and}  c+ a \geq ca. Prove that a+b+c≥34abc\displaystyle a + b + c \geq \frac34abc.
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