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Nice inequality: prove 4x+y+z>=2

Source: St. Petersburg Math Olympiad, 2015, round ii, grade 9, P4

September 30, 2016
inequalitiesinequalities proposedalgebra

Problem Statement

Positive numbers x,y,zx, y, z satisfy the condition xy+yz+zx+2xyz=1.xy + yz + zx + 2xyz = 1. Prove that 4x+y+z≥2.4x + y + z \ge 2.
A. Khrabrov
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