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5.

Part of 2023 Polish Junior Math Olympiad First Round

Problems(1)

2023 Polish Junior Math Olympiad Round 1 P5

Source:

5/21/2023
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.
inequalitiesalgebra