Let $\displaystyle x_{1},x_{2},...,x_{n}$ be positive real numbers. Prove that

$\displaystyle n^2\leq(x_1+x_2+...+x_n)(\frac{1}{x_1}+\frac{1}{x_ 2}+...+\frac{1}{x_n})$ and

$\displaystyle \frac{x_1+x_2+...+x_n}{\sqrt{n}}\leq\sqrt{(x_1)^2+ (x_2)^2+...+(x_n)^2}$

I really have no idea how to even begin this... any ideas?