Đáp án+Giải thích các bước giải:

$1)\\ A=\{x \in \mathbb{N}|(x^2+5x-6)(3x-x^2)=0\}\\ (x^2+5x-6)(3x-x^2)=0\\ \Leftrightarrow (x^2-x+6x-6)x(3-x)=0\\ \Leftrightarrow (x(x-1)+6(x-1))x(3-x)=0\\ \Leftrightarrow (x+6)(x-1)x(3-x)=0\\ \Leftrightarrow x=-6;x=1;x=0;x=3\\ x \in \mathbb{N} \Rightarrow A=\{0;1;3\}\\ B=\{x \in \mathbb{Z}|1 \le x^2 <10 \}\\ 1 \le x^2 <10\\ \Leftrightarrow\left\{\begin{array}{l} x^2 \ge 1\\  x^2<10\end{array} \right.\\ \Leftrightarrow \left\{\begin{array}{l} \left[\begin{array}{l} x \ge 1\\  x \le -1\end{array} \right. \\-\sqrt{10} < x <\sqrt{10}\end{array} \right.\\ \Leftrightarrow  \left[\begin{array}{l} 1 \le x <\sqrt{10} \\-\sqrt{10} < x \le -1\end{array} \right.\\ x \in \mathbb{Z} \Rightarrow x \in \{-3;-2;-1;1;2;3\}\\ A \cup B= \{-3;-2;-1;0;1;2;3\}\\ B \cap A=\{1;3\}\\ 2)\\ A=\{x \in \mathbb{N}|x=2k, k \in \mathbb{N}; k <3\}\\ k \in \mathbb{N}; k <3 \Rightarrow \in \{0;1;2\}\\ \Rightarrow 2k \in \{0;2;4\}\\ \Leftrightarrow  x \in \{0;2;4\}\\ \Rightarrow A= \{0;2;4\}\\ B=\{x \in \mathbb{Z}|x \le |x-1| <3\}\\ x \le |x-1| <3\\ \Leftrightarrow \left[\begin{array}{l} x \le x-1 <3(\text{Vô lí do } x>x-1 \ \forall \ x)\\ -3 \le x-1 <-x\end{array} \right.\\ \Leftrightarrow -3 \le x-1 <-x\\ \Leftrightarrow \left\{\begin{array}{l} x-1 \ge -3 \\ x-1 <-x\end{array} \right.\\ \Leftrightarrow \left\{\begin{array}{l} x \ge -2 \\ 2x <1\end{array} \right.\\ \Leftrightarrow \left\{\begin{array}{l} x \ge -2 \\ x <\dfrac{1}{2}\end{array} \right.\\ \Leftrightarrow  -2 \le  x <\dfrac{1}{2}\\ x \in \mathbb{Z} \Rightarrow x \in \{-2;-1;0\}\\ C=\{-1;2;3\}\\ B \cup C= \{-2;-1;0;2;3\}\\ A \cup (B \cup C) =\{-2;-1;0;2;3;4\}\\ B \cap C=\{-1\}\\ A \cap (B \cap C)=\varnothing.$