Three Absolute Dominations

★ 7/10Absolute Value algebra inequality Symmetry

Problem

Real numbers $a, b, c$ satisfy

|a| \geqslant |b + c|, \qquad |b| \geqslant |c + a|, \qquad |c| \geqslant |a + b|.

Prove that $a + b + c = 0$ .

Answer

Solution

Difficulty	7/10
Topics	Absolute Value, algebra, inequality, Symmetry

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