Đáp án:
\[x = 11\]
Giải thích các bước giải:
\(\begin{array}{l}
DKXD:\,\,\,x \ge 2\\
\sqrt {9x - 18} + \dfrac{1}{5}\sqrt {25x - 50} = 2\sqrt {x - 2} + 6\\
\Leftrightarrow \sqrt {9\left( {x - 2} \right)} + \dfrac{1}{5}\sqrt {25\left( {x - 2} \right)} = 2\sqrt {x - 2} + 6\\
\Leftrightarrow \sqrt {{3^2}.\left( {x - 2} \right)} + \dfrac{1}{5}.\sqrt {{5^2}.\left( {x - 2} \right)} = 2\sqrt {x - 2} + 6\\
\Leftrightarrow \sqrt {{3^2}} .\sqrt {x - 2} + \dfrac{1}{5}.\sqrt {{5^2}} .\sqrt {x - 2} = 2\sqrt {x - 2} + 6\\
\Leftrightarrow 3\sqrt {x - 2} + \dfrac{1}{5}.5\sqrt {x - 2} = 2\sqrt {x - 2} + 6\\
\Leftrightarrow 3\sqrt {x - 2} + \sqrt {x - 2} - 2\sqrt {x - 2} = 6\\
\Leftrightarrow 2\sqrt {x - 2} = 6\\
\Leftrightarrow \sqrt {x - 2} = 3\\
\Leftrightarrow x - 2 = {3^2}\\
\Leftrightarrow x - 2 = 9\\
\Leftrightarrow x = 11
\end{array}\)
