Question

Aratati ca oricare ar fi a,b,c avem:
|a+b|+|a+c| ≥|b-c|.

Answer 1

Vom folosi inegalitatea $|x|+|y| \geq |x-y|$.
Astfel: $|a+b|+|a+c| \geq |(a+b)-(a+c)|=|b-c|$.