[tex]\it 1.\ x\in\mathbb{N}^*\ \ \ \ \ \ (1)\\ \\ x^2+3x\leq4 \Rightarrow x(x+3)\leq 4=1\cdot(1+3) \Rightarrow x\leq1\ \ \ \ \ \ (2)\\ \\ (1),\ (2) \Rightarrow x=1 \Rightarrow A=\{1\}[/tex]
[tex]\it 2.\ 2x+3>0 \Rightarrow 2x>-3 \Rightarrow x> -\dfrac{3}{2} \Rightarrow x\in(-\dfrac{3}{2},\ \infty)\ \ \ \ \ \ (1)\\ \\ 2\leq x^2+4x+2|_{-2} \Rightarrow 0\leq x^2+4x \Rightarrow x^2+4x\geq0 \Rightarrow x(x+4)\geq0 \Rightarrow\\ \\ \Rightarrow x\in \mathbb{R}\setminus (-4,\ 0)\ \ \ \ \ (2)\\ \\ (1),\ (2) \Rightarrow S=[0,\ \infty)[/tex]
[tex]\it 3.\ \ x+y=3 \Rightarrow y=3-x\ \ \ \ \ \ (*)\\ \\ x^2+x=y\ \stackrel{(*)}{\Longrightarrow}\ x^2+x=3-x \Rightarrow x^2+2x-3=0 \Rightarrow x_1=-3,\ x_2=1\\ \\ (*) \Rightarrow y_1=6,\ y_2=2[/tex]
[tex]\it S=\{(-3,\ 6),\ (1,\ 2)\}[/tex]
