MathDB
absolute value inequality (Croatian MO 2004 1st Grade P3)

Source:

April 8, 2021
absolute valueinequalities

Problem Statement

Prove that for any three real numbers x,y,zx,y,z the following inequality holds: ∣x∣+∣y∣+∣z∣−∣x+y∣−∣y+z∣−∣z+x∣+∣x+y+z∣≥0.|x|+|y|+|z|-|x+y|-|y+z|-|z+x|+|x+y+z|\ge0.
Back to ProblemsView on AoPS