\(a,PT\Leftrightarrow\sqrt{3}\left(x+1\right)=2\sqrt{3}+3\sqrt{3}=5\sqrt{3}\\ \Leftrightarrow x+1=5\Leftrightarrow x=4\\ b,\Leftrightarrow\sqrt{3}x^2-2\sqrt{3}=0\\ \Leftrightarrow\sqrt{3}\left(x^2-2\right)=0\\ \Leftrightarrow\left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=\sqrt{2}\\x=-\sqrt{2}\end{matrix}\right.\\ c,\Leftrightarrow\left|x-3\right|=9\Leftrightarrow\left[{}\begin{matrix}x-3=9\\x-3=-9\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=12\\x=-6\end{matrix}\right.\\ d,\Leftrightarrow\left|2x+1\right|=6\Leftrightarrow\left[{}\begin{matrix}2x+1=6\\2x+1=-6\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=-\dfrac{7}{2}\end{matrix}\right.\)
