a) \(\Leftrightarrow2\sqrt{x-1}+\dfrac{2}{3}\sqrt{x-1}-4\sqrt{x-1}=\dfrac{10}{3}\left(đk:x\ge1\right)\)
\(\Leftrightarrow\dfrac{-4}{3}\sqrt{x-1}=\dfrac{10}{3}\)
\(\Leftrightarrow\sqrt{x-1}=-\dfrac{5}{2}\left(VLý.do.\sqrt{x-1}\ge0\forall x\right)\)
Vậy \(S=\varnothing\)
b) \(\Leftrightarrow\sqrt{\left(3x-5\right)^2}=2\)
\(\Leftrightarrow\left|3x-5\right|=2\)
\(\Leftrightarrow\left[{}\begin{matrix}3x-5=2\\3x-5=-2\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{8}{3}\\x=1\end{matrix}\right.\)
c) \(\Leftrightarrow\left(\sqrt{x}-3\right)\left(2\sqrt{x}+5\right)=0\left(đk:x\ge0\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x}=3\\\sqrt{x}=-\dfrac{5}{2}\left(VLý\right)\end{matrix}\right.\)\(\Leftrightarrow x=9\left(tm\right)\)
