Đáp án:
\(S = \left\{ {7} \right\}\).
Giải thích các bước giải:
\(\begin{array}{l}\,\,\,\,\,\sqrt {4x - 12} + 2\sqrt {9x - 27} - \sqrt {36} = \sqrt {25x - 75} \,\,\left( {x \ge 3} \right)\\ \Leftrightarrow \sqrt {4\left( {x - 3} \right)} + 2\sqrt {9\left( {x - 3} \right)} - 6 = \sqrt {25\left( {x - 3} \right)} \\ \Leftrightarrow 2\sqrt {x - 3} + 6\sqrt {x - 3} - 6 = 5\sqrt {x - 3} \\ \Leftrightarrow 2\sqrt {x - 3} + 6\sqrt {x - 3} - 5\sqrt {x - 3} = 6\\ \Leftrightarrow \left( {2 + 6 - 5} \right)\sqrt {x - 3} = 6\\ \Leftrightarrow 3\sqrt {x - 3} = 6\\ \Leftrightarrow \sqrt {x - 3} = 2\\ \Leftrightarrow x - 3 = 4\\ \Leftrightarrow x = 7\,\,\left( {tm} \right)\end{array}\)
Vậy \(S = \left\{ {7} \right\}\).
