Giải thích các bước giải:
1)
\[\begin{array}{l}
a,\\
\sqrt {18} - 2\sqrt {50} + 3\sqrt 8 = \sqrt {{{2.3}^2}} - 2\sqrt {{{2.5}^2}} + 3\sqrt {{{2.2}^2}} = 3\sqrt 2 - 10\sqrt 2 + 6\sqrt 2 = - \sqrt 2 \\
b,\\
{\left( {\sqrt 7 - \sqrt 3 } \right)^2} + \sqrt {84} = 7 - 2\sqrt {21} + 3 + \sqrt {{{21.2}^2}} = 10\\
c,\\
\left( {\frac{{6 - 2\sqrt 2 }}{{3 - \sqrt 2 }} - \frac{5}{{\sqrt 5 }}} \right):\frac{1}{{2 - \sqrt 5 }} = \left( {2 - \sqrt 5 } \right).\left( {2 - \sqrt 5 } \right) = {\left( {2 - \sqrt 5 } \right)^2} = 4 - 4\sqrt 5 + 5 = 9 - 4\sqrt 5
\end{array}\]
2,
\[\begin{array}{l}
a,\\
\sqrt {{{\left( {2x + 3} \right)}^2}} = 4 \Leftrightarrow \left[ \begin{array}{l}
2x + 3 = 4\left( {x \ge \frac{{ - 3}}{2}} \right)\\
2x + 3 = - 4\left( {x < \frac{{ - 3}}{2}} \right)
\end{array} \right.\\
b,\\
\sqrt {9x} - 5\sqrt x = 6 - 4\sqrt x \\
\Leftrightarrow 3\sqrt x - 5\sqrt x = 6 - 4\sqrt x \\
\Leftrightarrow 2\sqrt x = 6\\
\Leftrightarrow x = 9
\end{array}\]
3)
\[\begin{array}{l}
a,\\
Q = \left( {\frac{1}{{\sqrt a + 1}} - \frac{1}{{a + \sqrt a }}} \right):\frac{{\sqrt a - 1}}{{a + 2\sqrt a + 1}}\\
DK{\rm{XD: a > 0}}\\
\Leftrightarrow {\rm{Q = }}\left( {\frac{1}{{\sqrt a + 1}} - \frac{1}{{\sqrt a \left( {\sqrt a + 1} \right)}}} \right):\frac{{\sqrt a - 1}}{{{{\left( {\sqrt a + 1} \right)}^2}}}\\
\Leftrightarrow Q = \left( {\frac{{\sqrt a - 1}}{{\sqrt a \left( {\sqrt a + 1} \right)}}} \right).\frac{{{{\left( {\sqrt a + 1} \right)}^2}}}{{\sqrt a - 1}}\left( {a \ne 1} \right)\\
\Leftrightarrow Q = \frac{{\sqrt a + 1}}{{\sqrt a }} = 1 + \frac{1}{{\sqrt a }}\\
b,\\
Q > 2 \Leftrightarrow \frac{1}{{\sqrt a }} > 1 \Leftrightarrow a < 1
\end{array}\]
