a, \(3x^2+2x-1=0\)
\(\Rightarrow x=\dfrac{-2\pm\sqrt{2^2-4.3.\left(-1\right)}}{2.3}=\dfrac{-2\pm\sqrt{4+12}}{6}=\dfrac{-2\pm\sqrt{16}}{6}\)
\(\Rightarrow x=\dfrac{-2\pm4}{6}\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{-2+4}{6}\\x=\dfrac{-2-4}{6}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{3}\\x=-1\end{matrix}\right.\)
b, \(x^2-5x+6=0\)
\(\Rightarrow x=\dfrac{5\pm\sqrt{\left(-5\right)^2-4.1.6}}{2.1}=\dfrac{5\pm\sqrt{25-24}}{2}\)
\(\Rightarrow x=\dfrac{5\pm\sqrt{1}}{2}=\dfrac{5\pm1}{2}\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{5+1}{2}\\x=\dfrac{5-1}{2}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=3\\x=2\end{matrix}\right.\)
c, \(x^2-3x+2=0\)
\(\Rightarrow x=\dfrac{3\pm\sqrt{\left(-3\right)^2-4.1.2}}{2.1}=\dfrac{3\pm\sqrt{\left(9-8\right)}}{2}=\dfrac{3\pm\sqrt{1}}{2}=\dfrac{3\pm1}{2}\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{3+1}{2}\\x=\dfrac{3-1}{2}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=2\\x=1\end{matrix}\right.\)
d, \(2x^2-6x+1=0\)
\(\Rightarrow x=\dfrac{6\pm\sqrt{\left(-6\right)^2-4.2.1}}{2.2}=\dfrac{6\pm\sqrt{36-8}}{4}=\dfrac{6\pm\sqrt{28}}{4}\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{6+2\sqrt{7}}{4}\\x=\dfrac{6-2\sqrt{7}}{4}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{3+\sqrt{7}}{4}\\x=\dfrac{3-\sqrt{7}}{4}\end{matrix}\right.\)
