Đáp án:

$1\\a) A=\{-3;0;1\}\\ b)B=\left\{\dfrac{3-\sqrt{21}}{2};1;\dfrac{3+\sqrt{21}}{2} \right\}\\ c)C =\{-3;1;2;3\}\\ 2)$

 $C$ là tập rỗng

$3)\\ a): \varnothing; \{1\}; \{2\}; \{1;2\}\\ b)\varnothing; \{a\}; \{b\}; \{c\};\{a;b\}; \{b;c\}; \{c;a\}; \{a;b;c\}\\ c)\varnothing; \{1\}; \{5\}; \{a\};\{b\}; \{1;5\}; \{1;a\}; \{1;b\}; \{5;a\} ; \{5;b\}; \{a;b\};\{1;5;a\}; \{1;5;b\}; \{5;a;b\}; \{1;a;b\}; \{1;5;a;b\}.$

Giải thích các bước giải:

$1\\a)A=\{x \in \mathbb{R}|(x-x^2)(-x^2-2x+3)=0\}\\ (x-x^2)(-x^2-2x+3)=0\\ \Leftrightarrow (x^2-x)(x^2+2x-3)=0\\ \Leftrightarrow x(x-1)(x^2-x+3x-3)=0\\ \Leftrightarrow x(x-1)(x(x-1)+3(x-1))=0\\ \Leftrightarrow x(x-1)(x+3)(x-1)=0\\ \Leftrightarrow x(x-1)^2(x+3)=0\\ \Leftrightarrow \left[\begin{array}{l} x=0\\ x=1 \\ x=-3\end{array} \right.\\ \Rightarrow A=\{-3;0;1\}\\ b)B=\{x \in \mathbb{Z}|-2x^3+8x^2-6=0\}\\ -2x^3+8x^2-6=0\\ \Leftrightarrow -2x^3+2x^2+6x^2-6x+6x-6=0\\ \Leftrightarrow -2x^2(x-1)+6x(x-1)+6(x-1)=0\\ \Leftrightarrow (x-1)(-2x^2+6x+6)=0\\ \Leftrightarrow \left[\begin{array}{l} x=1\\ -2x^2+6x+6=0\end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} x=1\\ x=\dfrac{3+\sqrt{21}}{2} \\ x=\dfrac{3-\sqrt{21}}{2} \end{array} \right.\\ \Rightarrow B=\left\{\dfrac{3-\sqrt{21}}{2};1;\dfrac{3+\sqrt{21}}{2} \right\}\\ c)C=\{x \in \mathbb{N}| x^4-3x^3-7x^2+27x-18=0\}\\ x^4-3x^3-7x^2+27x-18=0\\ \Leftrightarrow x^4-x^3-2x^3+2x^2-9x^2+9x+18x-18=0\\ \Leftrightarrow x^3(x-1)-2x^2(x-1)-9x(x-1)+18(x-1)=0\\ \Leftrightarrow (x-1)(x^3-2x^2-9x+18)=0\\ \Leftrightarrow (x-1)(x^2(x-2)-9(x-2))=0\\ \Leftrightarrow (x-1)(x^2-9)(x-2)=0\\ \Leftrightarrow (x-1)(x-3)(x+3)(x-2)=0\\ \Leftrightarrow \left[\begin{array}{l} x=-3\\x=1\\x=2\\x=3\end{array} \right.\\ \Rightarrow C=\{-3;1;2;3\}\\ 2)\\ a)B=\{x \in \mathbb{Z}|2x^2-4x+\dfrac{3}{2}=0\}\\  2x^2-4x+\dfrac{3}{2}=0\\ \Leftrightarrow \left[\begin{array}{l} x=\dfrac{3}{2}\\ x=\dfrac{1}{2}\end{array} \right.\\ \Rightarrow B=\left\{\dfrac{1}{2};\dfrac{3}{2}\right\}\\ b)C=\{x \in \mathbb{R}|5x^2-6x+19=0\}\\ 5x^2-6x+19=0(\text{Vô nghiệm})\\ \Rightarrow C=\varnothing\\ c)D=\{x \in \mathbb{N}|x^3+3x^2+x+3=0\}\\ x^3+3x^2+x+3=0\\ \Leftrightarrow x^2(x+3)+(x+3)=0\\ \Leftrightarrow (x+3)(x^2+1)=0\\  \Leftrightarrow \left[\begin{array}{l} x=-3\\ x^2+1=0(\text{Vô nghiệm})  \end{array} \right.$

Vậy $C$ là tập rỗng

$3)\\ a)A=\{1;2\}$

Các tập con: $\varnothing; \{1\}; \{2\}; \{1;2\}$

$b)B=\{a;b;c\}$

Các tập con: $\varnothing; \{a\}; \{b\}; \{c\};\{a;b\}; \{b;c\}; \{c;a\}; \{a;b;c\}$

$c)C=\{1;5;a;b\}$

Các tập con:

$\varnothing; \{1\}; \{5\}; \{a\};\{b\}; \{1;5\}; \{1;a\}; \{1;b\}; \{5;a\} ; \{5;b\}; \{a;b\};\{1;5;a\}; \{1;5;b\}; \{5;a;b\}; \{1;a;b\}; \{1;5;a;b\}.$