Can someone show me how to solve this inequality, could AM/GM be of any use?
$\displaystyle
(a_0+a_1+...+a_n)^2+(a_0-a_1+...-a_n)^2\leq (n+2)(a_0^2+a_1^2+...+a_n^2)
$
Use:
$\displaystyle (x_0+x_1+\ldots +x_n)^2=\displaystyle\sum_{0\leq i \leq n}{x_i^2}+2\displaystyle\sum_{0\leq i<j\leq n}{x_ix_j}$
and simplify the left side.
Fernando Revilla