Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
\sqrt {10 + \sqrt {3x} } = 2 + \sqrt 6 \,\,\,\,\,\,\,\,\,\,\,\left( {x \ge 0} \right)\\
\Leftrightarrow 10 + \sqrt {3x} = {\left( {2 + \sqrt 6 } \right)^2}\\
\Leftrightarrow 10 + \sqrt {3x} = 2 + 2.2.\sqrt 6 + 6\\
\Leftrightarrow 10 + \sqrt {3x} = 8 + 4\sqrt 6 \\
\Leftrightarrow \sqrt {3x} = 4\sqrt 6 - 2\\
\Leftrightarrow 3x = {\left( {4\sqrt 6 - 2} \right)^2}\\
\Leftrightarrow 3x = 96 - 2.4\sqrt 6 .2 + 4\\
\Leftrightarrow 3x = 100 - 16\sqrt 6 \\
\Leftrightarrow x = \frac{{100 - 16\sqrt 6 }}{3}\\
b,\\
\sqrt {4x + 20} - 3\sqrt {5 + x} + \frac{4}{3}\sqrt {9x + 45} = 6\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {x \ge - 5} \right)\\
\Leftrightarrow \sqrt {4.\left( {x + 5} \right)} - 3\sqrt {x + 5} + \frac{4}{3}.\sqrt {9\left( {x + 5} \right)} = 6\\
\Leftrightarrow 2.\sqrt {x + 5} - 3\sqrt {x + 5} + \frac{4}{3}.3.\sqrt {x + 5} = 6\\
\Leftrightarrow \sqrt {x + 5} .\left( {2 - 3 + \frac{4}{3}.3} \right) = 6\\
\Leftrightarrow 3\sqrt {x + 5} = 6\\
\Leftrightarrow \sqrt {x + 5} = 2\\
\Leftrightarrow x + 5 = 4\\
\Leftrightarrow x = - 1\\
c,\\
\sqrt {x + 1} \ge \sqrt 5 \,\,\,\,\,\,\,\,\,\,\,\,\left( {x \ge - 1} \right)\\
\Leftrightarrow x + 1 \ge 5\\
\Leftrightarrow x \ge 4
\end{array}\)
