a/ \(\left(2x\right)^2-2.2x.3+3^2-16=0\)
\(\Leftrightarrow\left(2x-3\right)^2=16\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-3=4\\2x-3=-4\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}2x=7\\2x=-1\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=\dfrac{7}{2}\\x=\dfrac{-1}{2}\end{matrix}\right.\)
b/ \(x^2+2\sqrt{3}.x+\left(\sqrt{3}\right)^2-4=0\)
\(\Leftrightarrow\left(x+\sqrt{3}\right)^2=4\)
\(\Leftrightarrow\left[{}\begin{matrix}x+\sqrt{3}=2\\x+\sqrt{3}=-2\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=2-\sqrt{3}\\x=-2-\sqrt{3}\end{matrix}\right.\)
c/ \(3x^2-6x+3-2=0\)
\(\Leftrightarrow3\left(x^2-2x+1\right)=2\)
\(\Leftrightarrow\left(x-1\right)^2=\dfrac{2}{3}\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=\dfrac{\sqrt{6}}{3}\\x-1=\dfrac{-\sqrt{6}}{3}\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=\dfrac{3+\sqrt{6}}{3}\\x=\dfrac{3-\sqrt{6}}{3}\end{matrix}\right.\)
d/ \(\left(\sqrt{2}x\right)^2-2.2.\left(\sqrt{2}x\right)+2^2-2=0\)
\(\Leftrightarrow\left(\sqrt{2}x-2\right)^2=2\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{2}x-2=\sqrt{2}\\\sqrt{2}x-2=-\sqrt{2}\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}\sqrt{2}x=2+\sqrt{2}\\\sqrt{2}x=2-\sqrt{2}\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=\sqrt{2}+1\\x=\sqrt{2}-1\end{matrix}\right.\)
