|x+y2+√xy|+|x+y2−√xy|=|x+y+2√xy2|+|x+y−2√xy2|=√x+√y2+√x−√y2$=\sqrt{x}$
$\left| {\frac{x+y}{2}+\sqrt{xy}} \right|+\left| {\frac{x+y}{2}-\sqrt{xy}} \right|=\left| {\frac{x+y+2\sqrt{xy}}{2}} \right|+\left| {\frac{x+y-2\sqrt{xy}}{2}} \right|=\frac{(\sqrt{x}+\sqrt{y})^2}{2}+\frac{(\sqrt{x}-\sqrt{y})^2}{2}$$=x+y=|x|+|y|vớixy \ge 0.$