Giải thích các bước giải:
a.Ta có :
$P=1+\dfrac{2xy\sqrt x+2xy\sqrt y}{ \sqrt x+ \sqrt y}:(\dfrac{2xy}{x+\sqrt{xy}} +\dfrac{2xy}{y+ \sqrt{xy}})$
$\to P=1+\dfrac{2xy(\sqrt x+\sqrt y)}{ \sqrt x+ \sqrt y}:(\dfrac{2y\sqrt{x}}{\sqrt{x}+\sqrt{y}} +\dfrac{2x\sqrt{y}}{\sqrt{x}+\sqrt{y}})$
$\to P=1+2xy:\dfrac{2\sqrt{y}\sqrt{x}(\sqrt{y}+\sqrt{x})}{\sqrt{x}+\sqrt{y}}$
$\to P=1+2xy:(2\sqrt{xy})$
$\to P=1+\sqrt{xy}$
b.Từ câu a $\to 1+\sqrt{xy}=m\to \sqrt{xy}=m-1\to m\ge 1$
Mà $\sqrt{xy}\le \dfrac{(\sqrt{x}+\sqrt{y})^2}{4}=9\to m-1\le 9\to m\le 10$
$\to 1\le m\le 10$