\[\begin{array}{l}
1)\,\,\sqrt {4x - 1} - \sqrt {4x} - 2\sqrt 3 = 0\,\,\,xem\,\,\,lai\,\,\,de\,\,\,bai.\\
2)\,\, - \sqrt {9 + 4\sqrt 5 } + \sqrt {5x + 2} = 0\\
DK:\,\,\,x \ge - \frac{2}{5}\\
pt \Leftrightarrow \sqrt {5x + 2} = \sqrt {9 + 4\sqrt 5 } \\
\Leftrightarrow 5x + 2 = 9 + 4\sqrt 5 \\
\Leftrightarrow 5x = 7 + 4\sqrt 5 \\
\Leftrightarrow x = \frac{{7 + 4\sqrt 5 }}{2}\,\,\,\left( {tm} \right).\\
3)\,\,\,\sqrt {50x - 25} + \sqrt {4x + 4} = \sqrt {16x + 16} - \sqrt {32x - 16} \\
DK:\,\,\,x \ge \frac{1}{2}\\
pt \Leftrightarrow \sqrt {25\left( {2x - 1} \right)} + \sqrt {4\left( {x + 1} \right)} = \sqrt {16\left( {x + 1} \right)} - \sqrt {16\left( {2x - 1} \right)} \\
\Leftrightarrow 5\sqrt {2x - 1} + 4\sqrt {2x - 1} = 4\sqrt {x + 1} - 2\sqrt {x + 1} \\
\Leftrightarrow 9\sqrt {2x - 1} = 2\sqrt {x + 1} \\
\Leftrightarrow 81\left( {2x - 1} \right) = 4\left( {x + 1} \right)\\
\Leftrightarrow 162x - 81 = 4x + 4\\
\Leftrightarrow 158x = 89\\
\Leftrightarrow x = \frac{{89}}{{158}}\,\,\,\left( {tm} \right)\\
4)\,\,\,\sqrt {{x^2} + 2x\sqrt 5 + 5} - \sqrt {6 - 2\sqrt 5 } = 0\\
\Leftrightarrow \sqrt {{{\left( {x + \sqrt 5 } \right)}^2}} = \sqrt {6 - 2\sqrt 5 } \\
\Leftrightarrow \sqrt {{{\left( {x + \sqrt 5 } \right)}^2}} = \sqrt {{{\left( {\sqrt 5 - 1} \right)}^2}} \\
\Leftrightarrow \left[ \begin{array}{l}
x + \sqrt 5 = \sqrt 5 - 1\\
x + \sqrt 5 = 1 - \sqrt 5
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = - 1\\
x = 1 - 2\sqrt 5
\end{array} \right..
\end{array}\]
