Đáp án:
$\displaystyle \begin{array}{{>{\displaystyle}l}} 2.\ M=\frac{3\sqrt{x}}{\sqrt{x} +3}\\ 3.\ 0\leqslant x< \frac{9}{2} ,\ x\neq 1 \end{array}$
Giải thích các bước giải:
$\displaystyle \begin{array}{{>{\displaystyle}l}} 2.M=\ \frac{2\sqrt{x}\left(\sqrt{x} -3\right) +\sqrt{x}\left(\sqrt{x} +3\right)}{\left(\sqrt{x} +3\right)\left(\sqrt{x} -3\right)} .\frac{\sqrt{x} -3}{\sqrt{x} -1}\\ M=\frac{3x-3\sqrt{x}}{\left(\sqrt{x} +3\right)\left(\sqrt{x} -3\right)} .\frac{\sqrt{x} -3}{\sqrt{x} -1}\\ M=\frac{3\sqrt{x}\left(\sqrt{x} -1\right)}{\left(\sqrt{x} +3\right)\left(\sqrt{x} -3\right)} .\frac{\sqrt{x} -3}{\sqrt{x} -1}\\ M=\frac{3\sqrt{x}}{\sqrt{x} +3}\\ 3.\ M< \sqrt{M}\\ \Leftrightarrow \frac{3\sqrt{x}}{\sqrt{x} +3} -\sqrt{\frac{3\sqrt{x}}{\sqrt{x} +3}} < 0\\ \Leftrightarrow \sqrt{\frac{3\sqrt{x}}{\sqrt{x} +3}}\left(\sqrt{\frac{3\sqrt{x}}{\sqrt{x} +3}} -1\right) < 0\\ \Leftrightarrow 0< \sqrt{\frac{3\sqrt{x}}{\sqrt{x} +3}} < 1\\ \Rightarrow 0< \frac{3\sqrt{x}}{\sqrt{x} +3} < 1\\ \Leftrightarrow \frac{3\sqrt{x}}{\sqrt{x} +3} -1< 0\\ \Leftrightarrow \frac{3\sqrt{x} -\sqrt{x} -3}{\sqrt{x} +3} < 0\\ \Leftrightarrow 2\sqrt{x} -3< 0\\ \Leftrightarrow \sqrt{x} < \frac{3}{2}\\ \Leftrightarrow x< \frac{9}{2} \ kết\ hợp\ với\ ĐKXD\\ \Rightarrow 0\leqslant x< \frac{9}{2} ,\ x\neq 1 \end{array}$
