MathDB

2

Part of 2020 Junior Macedonian National Olympiad

Problems(1)

2020 Macedonian Junior BMO TST- P2

Source: 2020 Junior Macedonian Mathematical Olympiad

9/7/2020
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?
easyInequalityAM-GMjmmo2020