Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
1,\\
P = \dfrac{{\sqrt x + 1}}{{2\sqrt x }}\\
P - \dfrac{1}{2} = \dfrac{{\sqrt x + 1}}{{2\sqrt x }} - \dfrac{1}{2} = \dfrac{{\left( {\sqrt x + 1} \right) - \sqrt x }}{{2\sqrt x }} = \dfrac{1}{{2\sqrt x }}\\
\sqrt x > 0,\,\,\,\forall x > 0 \Rightarrow \dfrac{1}{{2\sqrt x }} > 0,\,\,\,\forall x > 0\\
\Rightarrow P - \dfrac{1}{2} > 0,\,\,\,\forall x\\
\Rightarrow P > \dfrac{1}{2},\,\,\,\forall x\\
2,\\
M = \dfrac{{\sqrt x - 2}}{{\sqrt x }}\\
M - 1 = \dfrac{{\sqrt x - 2}}{{\sqrt x }} - 1 = \dfrac{{\left( {\sqrt x - 2} \right) - \sqrt x }}{{\sqrt x }} = \dfrac{{ - 2}}{{\sqrt x }}\\
\sqrt x > 0,\,\,\,\forall x > 0 \Rightarrow \dfrac{{ - 2}}{{\sqrt x }} < 0,\,\,\,\forall x > 0\\
\Rightarrow M - 1 < 0,\,\,\forall x > 0\\
\Rightarrow M < 1,\,\,\,\forall x > 0
\end{array}\)
