Đáp án:
$\begin{array}{l}
d)D = \left( {\dfrac{{6 - 2\sqrt 2 }}{{3 - \sqrt 2 }} - \dfrac{5}{{\sqrt 5 }}} \right):\dfrac{1}{{2 - \sqrt 5 }}\\
= \left( {\dfrac{{2.\left( {3 - \sqrt 2 } \right)}}{{3 - \sqrt 2 }} - \sqrt 5 } \right).\left( {2 - \sqrt 5 } \right)\\
= \left( {2 - \sqrt 5 } \right).\left( {2 - \sqrt 5 } \right)\\
= {\left( {2 - \sqrt 5 } \right)^2}\\
= 4 - 2.2.\sqrt 5 + 5\\
= 9 - 4\sqrt 5 \\
4)\\
g)DKxd:\left\{ \begin{array}{l}
3x + 1 \ge 0\\
4x - 3 \ge 0
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
x \ge - \dfrac{1}{3}\\
x \ge \dfrac{3}{4}
\end{array} \right. \Rightarrow x \ge \dfrac{3}{4}\\
\sqrt {3x + 1} = \sqrt {4x - 3} \\
\Rightarrow 3x + 1 = 4x - 3\\
\Rightarrow x = 4\left( {tmdk} \right)\\
\text{Vậy}\,x = 4\\
h)Dkxd:x \ge 0\\
7\sqrt {2x} - 2\sqrt {2x} - 4 = 3\sqrt {2x} \\
\Rightarrow 5\sqrt {2x} - 3\sqrt {2x} = 4\\
\Rightarrow 2\sqrt {2x} = 4\\
\Rightarrow \sqrt {2x} = 2\\
\Rightarrow 2x = 4\\
\Rightarrow x = 2\left( {tmdk} \right)\\
\text{Vậy}\,x = 2\\
i)Dkxd:x \ge - 2\\
\sqrt {9x + 18} - 5\sqrt {x + 2} + \dfrac{4}{5}\sqrt {25 + 50} = 6\\
\Rightarrow 3\sqrt {x + 2} - 5\sqrt {x + 2} + \dfrac{4}{5}.5\sqrt {x + 2} = 6\\
\Rightarrow 2\sqrt {x + 2} = 6\\
\Rightarrow \sqrt {x + 2} = 3\\
\Rightarrow x + 2 = 9\\
\Rightarrow x = 7\left( {tmdk} \right)\\
\text{Vậy}\,x = 7\\
k)DKxd:x \ge 5\\
\sqrt {9x - 45} + \sqrt {4x - 20} - \sqrt {x - 5} = 8\\
\Rightarrow 3\sqrt {x - 5} + 2\sqrt {x - 5} - \sqrt {x - 5} = 8\\
\Rightarrow 4\sqrt {x - 5} = 8\\
\Rightarrow \sqrt {x - 5} = 2\\
\Rightarrow x - 5 = 4\\
\Rightarrow x = 9\left( {tmdk} \right)\\
\text{Vậy}\,x = 9
\end{array}$
