Cho phương trình \({x^2} - 2\left( {m + 1} \right)x + 2m + 1 = 0\)
a) Giải phương trình khi \(m = 2\).
b) Tìm \(m\) để phương trình có hai nghiệm phân biệt \({x_1},\,{x_2}\) sao cho \(x_1^3 + x_2^3 = 2019\).
A.\(\begin{array}{l}{\rm{a)}}\,\,{x_1} = - 1\,\,;\,\,{x_2} = 5.\\{\rm{b)}}\,\,m = \frac{{\sqrt[3]{{2018}} + 1}}{2}\end{array}\)
B.\(\begin{array}{l}{\rm{a)}}\,\,{x_1} = 1\,\,;\,\,{x_2} = - 5.\\{\rm{b)}}\,\,m = \sqrt[3]{{2018}} - 1\end{array}\)
C.\(\begin{array}{l}{\rm{a)}}\,\,{x_1} = 1\,\,;\,\,{x_2} = 5.\\{\rm{b)}}\,\,m = \frac{{\sqrt[3]{{2018}} - 1}}{2}\end{array}\)
D.\(\begin{array}{l}{\rm{a)}}\,\,{x_1} = - 1\,\,;\,\,{x_2} = - 5.\\{\rm{b)}}\,\,m = \sqrt[3]{{2018}} + 1\end{array}\)