Cho 2 tập hợp A=(-∞;2020) và B={x ∈ Z| $x^{3}$ -2020 $x^{2}$ +2021 x=0} Xác định A ∩ B ; B \ A 23/11/2021 Bởi Sarah Cho 2 tập hợp A=(-∞;2020) và B={x ∈ Z| $x^{3}$ -2020 $x^{2}$ +2021 x=0} Xác định A ∩ B ; B \ A
`~rai~` $\begin{array}{I}x^3-2022x^2+2021=0\\\Leftrightarrow x(x^2-2022x+2021)=0\\\Leftrightarrow \left[\begin{array}{I}x=0\\x^2-2022x+2021=0\end{array}\right.\\\Leftrightarrow \left[\begin{array}{I}x=0\\x=1\\x=2021\end{array}\right.\\B=\{x\in \mathbb{Z}|x^3-2022x^2+2021x=0\}\Rightarrow B=\{0;1;2021\}\\A=(-\infty;2020)\\\Rightarrow A\cap B=\{0;1\}\\B\backslash A=\{2021\}.\end{array}$ Bình luận
Ta có: $x^3 – 2022x^2 + 2021x = 0$ $\to x(x^2 – 2022x + 2021)=0$ $\to \left[\begin{array}{l}x = 0\\x = 1\\x = 2021\end{array}\right.$ Ta được: $B =\{x\in \Bbb Z\Big|\, x^3 – 2020x^2 + 2021x = 0\}$ $\to B =\{0;1;2021\}$ $A = (-\infty;2020)$ $+)\quad A\cap B = \{0;1\}$ $+)\quad B\backslash A = \{2021\}$ Bình luận
`~rai~`
$\begin{array}{I}x^3-2022x^2+2021=0\\\Leftrightarrow x(x^2-2022x+2021)=0\\\Leftrightarrow \left[\begin{array}{I}x=0\\x^2-2022x+2021=0\end{array}\right.\\\Leftrightarrow \left[\begin{array}{I}x=0\\x=1\\x=2021\end{array}\right.\\B=\{x\in \mathbb{Z}|x^3-2022x^2+2021x=0\}\Rightarrow B=\{0;1;2021\}\\A=(-\infty;2020)\\\Rightarrow A\cap B=\{0;1\}\\B\backslash A=\{2021\}.\end{array}$
Ta có:
$x^3 – 2022x^2 + 2021x = 0$
$\to x(x^2 – 2022x + 2021)=0$
$\to \left[\begin{array}{l}x = 0\\x = 1\\x = 2021\end{array}\right.$
Ta được:
$B =\{x\in \Bbb Z\Big|\, x^3 – 2020x^2 + 2021x = 0\}$
$\to B =\{0;1;2021\}$
$A = (-\infty;2020)$
$+)\quad A\cap B = \{0;1\}$
$+)\quad B\backslash A = \{2021\}$