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2020 Macedonian Junior BMO TST- P2

Source: 2020 Junior Macedonian Mathematical Olympiad

September 7, 2020
easyInequalityAM-GMjmmo2020

Problem Statement

Let x,y,x, y, and zz be positive real numbers such that xy+yz+zx=27xy + yz + zx = 27. Prove that
x+y+z≥3xyzx + y + z \ge \sqrt{3xyz}.
When does equality hold?
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