Let $x_1, x_2, ..., x_{24}$ be real numbers. prove that $$x_1 + 2x_2 + 3x_3 +...+ 24x_{24} - 439 \le \frac{x^2_1+x^2_2+... + x^2_{24}}{2}+ 2011.$$
Source: 2011 Cuba MO 2.4
Tags: algebra, inequalities
Let $x_1, x_2, ..., x_{24}$ be real numbers. prove that $$x_1 + 2x_2 + 3x_3 +...+ 24x_{24} - 439 \le \frac{x^2_1+x^2_2+... + x^2_{24}}{2}+ 2011.$$