a)
[tex]\it \left.\begin{aligned} \it x\in(-2,\ 5) \Rightarrow -2 < x < 5\\ \\ \it y\in(-3,\ 4) \Rightarrow -3 < y < 4\end{aligned}\right\} \Rightarrow -5 < x+y < 9\\ \\ \\ -5 < x+y < 9\Big|_{-9} \Rightarrow -14 < x+y-9 < 0\\ \\ \\ -5 < x+y < 9\Big|_{+5} \Rightarrow 0 < x+y+5 < 14[/tex]
[tex]\it a=\sqrt{(x+y-9)^2}+\sqrt{(x+y+5)^2}=|\underbrace{x+y-9}_{ < 0}|+|\underbrace{x+y+5}_{ > 0}|=\\ \\ =-x-y+9+x+y+5=14\in\mathbb{N}[/tex]
