- Thread starter
- Admin
- #1
- Feb 14, 2012
- 3,973
If $a, b$ and $c$ are three real numbers such that $|a-b|\ge|c|$, $|b-c|\ge|a|$ and $|c-a|\ge|b|$, then prove that one of $a, b$ or $c$ is the sum of the other two.
Squaring both sides of the inequality of $|a-b|\ge|c|$, we getIf $a, b$ and $c$ are three real numbers such that $|a-b|\ge|c|$, $|b-c|\ge|a|$ and $|c-a|\ge|b|$, then prove that one of $a, b$ or $c$ is the sum of the other two.