\(a,ĐK:x\in R\\ \Leftrightarrow\left|3\left(x-2\right)\right|=12\\ \Leftrightarrow\left[{}\begin{matrix}3\left(x-2\right)=12\left(x\ge2\right)\\3\left(x-2\right)=-12\left(x< 2\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=6\left(x\ge2\right)\left(tm\right)\\x=-3\left(x< 2\right)\left(tm\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=6\\x=-3\end{matrix}\right.\)
\(b,\Leftrightarrow x\sqrt{5}=\sqrt{320}\Leftrightarrow5x^2=320\Leftrightarrow x^2=64\Leftrightarrow\left[{}\begin{matrix}x=8\\x=-8\end{matrix}\right.\)
\(c,ĐK:x\in R\\ \Leftrightarrow\left|5\left(2x-1\right)\right|=10\\ \Leftrightarrow\left[{}\begin{matrix}5\left(2x-1\right)=10\left(x\ge\dfrac{1}{2}\right)\\5\left(2x-1\right)=-10\left(x< \dfrac{1}{2}\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\left(tm\right)\\x=-\dfrac{1}{2}\left(tm\right)\end{matrix}\right.\)
\(d,ĐK:x\ge2\\ \Leftrightarrow6\sqrt{x-2}-3\sqrt{x-2}=-20+4\sqrt{x-2}\\ \Leftrightarrow\sqrt{x-2}=20\Leftrightarrow x-2=400\Leftrightarrow x=402\left(tm\right)\)
a) \(\sqrt{9.\left(x-2\right)^2}-12=0\)
\(\sqrt{3^2.\left(x-2\right)^2}-12=0\)
\(3\left(x-2\right)-12=0\)
\(3x-6=12\)
\(3x=18\)
\(x=6\)
b) \(\sqrt{5}.x-\sqrt{320}=0\)
\(\sqrt{5}.x-8.\sqrt{5}\)
\(\sqrt{5}\left(x-8\right)=0\)
\(x-8=0\)
\(x=8\)
c) \(\sqrt{25\left(4x^2-4x+1\right)}=10\)
\(\sqrt{5^2\left(2x-1\right)^2}=10\)
\(5\left(2x-1\right)=10\)
\(2x-1=2\)
\(2x=3\)
\(x=\dfrac{3}{2}\)
