a) \(9\sqrt{x+2}-\dfrac{1}{3}\sqrt{9x+18}=24\) (ĐK: \(x\ge-2\))
\(\Leftrightarrow9\sqrt{x+2}-\dfrac{1}{3}\sqrt{9\left(x+2\right)}=24\)
\(\Leftrightarrow9\sqrt{x+2}-\dfrac{1}{3}\cdot3\sqrt{x+2}=24\)
\(\Leftrightarrow9\sqrt{x+2}-\sqrt{x+2}=24\)
\(\Leftrightarrow8\sqrt{x+2}=24\)
\(\Leftrightarrow\sqrt{x+2}=\dfrac{24}{8}\)
\(\Leftrightarrow\sqrt{x+2}=3\)
\(\Leftrightarrow x+2=9\)
\(\Leftrightarrow x=9-2\)
\(\Leftrightarrow x=7\left(tm\right)\)
b) \(\sqrt{x^2-6x+9}-2=0\)
\(\Leftrightarrow\sqrt{\left(x-3\right)^2}=2\)
\(\Leftrightarrow\left|x-3\right|=2\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=-2\left(x< 3\right)\\x-3=2\left(x\ge3\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3-2\\x=3+2\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\left(tm\right)\\x=5\left(tm\right)\end{matrix}\right.\)
