Let a,b,c be three real numbers such that $|2a+2b+c| \le 1$, $|6a+3b+2c|\le 1$ and $|15a+10b+6c|\le 1$. Prove that $|a+b+c|\le 15$. When does the equality holds?
Well, I obtained that:
$15=7+5+3 \ge |(-7)(2a+2b+c)|+|(-5)(6a+3b+2c)|+|3(15a+10b+6c)| \ge |-14a-14b-7c-30a-15b-10c+45a+30b+18c|=|a+b+c|$
But, when the equality holds?
Well...it wasn't very hard! Sorry for posting this problem