Đáp án:
Giải thích các bước giải:
\(\begin{array}{l}
a.M = \frac{{\left( {\sqrt x - 2} \right)\left( {\sqrt x + 1} \right) - \left( {\sqrt x + 2} \right)\left( {\sqrt x - 1} \right)}}{{\left( {\sqrt x - 1} \right){{\left( {\sqrt x + 1} \right)}^2}}}.\frac{{{{\left( {1 - x} \right)}^3}}}{2}\\
= \frac{{x - \sqrt x - 2 - x - \sqrt x + 2}}{{ - \left( {1 - x} \right)\left( {\sqrt x + 1} \right)}}.\frac{{{{\left( {1 - x} \right)}^3}}}{2}\\
= \frac{{2\sqrt x }}{{\sqrt x + 1}}.\frac{{{{\left( {1 - x} \right)}^2}}}{2} = \frac{{\sqrt x {{\left( {1 - x} \right)}^2}}}{{\sqrt x + 1}}\\
b.M > 0\\
\to \frac{{\sqrt x {{\left( {1 - x} \right)}^2}}}{{\sqrt x + 1}} > 0\\
\to \left\{ \begin{array}{l}
\sqrt x > 0\\
\sqrt x + 1 > 0\\
x \ne 1
\end{array} \right. \to \left\{ \begin{array}{l}
x > 0\\
x \ne 1
\end{array} \right.
\end{array}\)
