Đáp án:
\(m=0\)
Giải thích các bước giải:
\(\begin{array}{l}
B \subset A\\
TH1:\,\,{x^2} - 2x + m = 0\,\,vo\,\,nghiem\\
\Rightarrow \Delta ' = 1 - m < 0 \Leftrightarrow m < 1\\
TH2:\,\,{x^2} - 2x + m = 0\,\,\left( * \right)\,\,co\,\,nghiem\,\,thuoc\,\,B.\\
+ )\,\,x = - 1\,\,la\,\,nghiem\,\,cua\,\,\left( * \right) \Rightarrow {\left( { - 1} \right)^2} - 2\left( { - 1} \right) + m = 0 \Leftrightarrow m = - 3\\
Thu\,\,lai:\,\,m = - 3 \Rightarrow {x^2} - 2x - 3 = 0 \Leftrightarrow \left[ \begin{array}{l}
x = - 1\\
x = 3
\end{array} \right.\\
\Rightarrow A = \left\{ { - 1;3} \right\}\,\,khong\,\,la\,\,con\,\,cua\,\,B \Rightarrow Loai.\\
+ )\,\,x = 0\,\,la\,\,nghiem\,\,cua\,\,\left( * \right) \Rightarrow m = 0\\
Thu\,\,lai:\,\,m = 0 \Rightarrow {x^2} - 2x = 0 \Leftrightarrow \left[ \begin{array}{l}
x = 0\\
x = 2
\end{array} \right.\\
\Rightarrow A = \left\{ {0;2} \right\} \subset B\,\,\left( {tm} \right)\\
+ )\,\,x = 2\,\,la\,\,nghiem\,cua\,\,\left( * \right) \Rightarrow {2^2} - 2.2 + m = 0 \Leftrightarrow m = 0\,\,\left( {tm} \right)\\
Vay\,\,m = 0.
\end{array}\)
