f, \(4x^2-12x+9=0\)
\(\Rightarrow\left(2x-3\right)^2=0\)
\(\Rightarrow2x-3=0\)
\(\Rightarrow2x=3\)
\(\Rightarrow x=\dfrac{3}{2}\)
g, \(3x^2+7x+2=0\)
\(\Rightarrow x=\dfrac{-7\pm\sqrt{7^2-4.3.2}}{2.3}=\dfrac{-7\pm49-24}{6}=\dfrac{-7\pm\sqrt{25}}{6}=\dfrac{-7\pm5}{6}\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{-7+5}{6}\\x=\dfrac{-7-5}{6}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{-1}{3}\\x=-2\end{matrix}\right.\)
\(\Rightarrow x_1=\dfrac{-1}{3};x_2=-2\)
h, \(x^2-4x+1=0\)
\(\Rightarrow\dfrac{4\pm\sqrt{\left(-4\right)^2-4.1.1}}{2.1}=\dfrac{4\pm\sqrt{16-4}}{2}=\dfrac{4\pm\sqrt{12}}{2}=\dfrac{4\pm2\sqrt{3}}{2}\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{4+2\sqrt{3}}{2}\\x=\dfrac{4-2\sqrt{3}}{2}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=2+\sqrt{3}\\x=2-\sqrt{3}\end{matrix}\right.\)
\(\Rightarrow x_1=2+\sqrt{3};x_2=2-\sqrt{3}\)
i, \(2x^2-6x+1=0\)
\(\Rightarrow x=\dfrac{6\pm\sqrt{\left(-6\right)^2-4.2.1}}{2.2}=\dfrac{6\pm\sqrt{36-8}}{4}=\dfrac{6\pm\sqrt{28}}{4}=\dfrac{6\pm2\sqrt{7}}{4}\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{6+2\sqrt{7}}{4}\\x=\dfrac{6-2\sqrt{7}}{4}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{3+\sqrt{7}}{2}\\x=\dfrac{3-\sqrt{7}}{2}\end{matrix}\right.\)
\(\Rightarrow x_1=\dfrac{3+\sqrt{7}}{2};x_2=\dfrac{3-\sqrt{7}}{2}\)
j, \(3x^2+4x-4=0\)
\(\Rightarrow x=\dfrac{-4\pm\sqrt{4^2-4.3.\left(-4\right)}}{2.3}=\dfrac{-4\pm\sqrt{16+68}}{6}=\dfrac{-4\pm\sqrt{64}}{6}=\dfrac{-4\pm8}{6}\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{-4+8}{6}\\x=\dfrac{-4-8}{6}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{2}{3}\\x=-2\end{matrix}\right.\)
\(\Rightarrow x_1=\dfrac{2}{3};x_2=-2\)
