19.Theo C-S
$VP^{2}\leq 2(2x^{2}+2y^{2}+2z^{2}+2t^{2})\leq 8$
18.$\Leftrightarrow \sum (x-y)^{2}\geq 0$
17.AM-GM
$\sum \frac{1}{x}\geq \frac{9}{\sum x}$
$\sum x +\frac{1}{\sum x}+\frac{8}{\sum x}\geq 2+8=10$
13.$\sum \sqrt{x^{2}+xy+y^{2}}\geq \sqrt{3}(\sum x)$
Ta sẽ chứng minh
$\sqrt{3}\left ( \sum x \right )^{2}\geq 3\sqrt{3}\left ( \sum xy\right )\Leftrightarrow (\sum x)^{2}\geq 3\left ( \sum xy \right )$