Question 75
1. Let $a$, $b$ and $c$ three real numbers such as $$
|a| \geqslant |a+b|,\ |b| \geqslant |b+c| \text{ and } |c| \geqslant |c+a|.
$$ show that $a = b = c = 0$. 2. Let $a$, $b$, $c$ and $d$ four real numbers such that $$
| a | \geqslant | a+b | ,\ | b | \geqslant | b+c | ,\ | c | \geqslant | c+d | \text{ and } | d | \geqslant | d+a |
$$ has necessarily $a = b = c = d = 0$?
|a| \geqslant |a+b|,\ |b| \geqslant |b+c| \text{ and } |c| \geqslant |c+a|.
$$ show that $a = b = c = 0$. 2. Let $a$, $b$, $c$ and $d$ four real numbers such that $$
| a | \geqslant | a+b | ,\ | b | \geqslant | b+c | ,\ | c | \geqslant | c+d | \text{ and } | d | \geqslant | d+a |
$$ has necessarily $a = b = c = d = 0$?