[tex]\it (a,\ b)=7 \Rightarrow \begin{cases} \it a=7x\\ \\ \it b=7y\\ \\ \it (x,\ y)=1\end{cases}\ \ \ \ \ (1)\\ \\ \\ a\cdot b=294\ \stackrel{(1)}{\Longrightarrow}\ 7x\cdot7y=294 \Rightarrow 49xy=294|_{:49} \Rightarrow xy=6=1\cdot6=2\cdot3=\\ \\ =3\cdot2=6\cdot1\ \ \ \ (2)\\ \\ (1),\ (2) \Rightarrow (a,\ b)\in\{(7,\ 42);\ (14,\ 21);\ (21,\ 14);\ (42,\ 7)\}[/tex]
[tex]\it a+b\in\{49,\ \ 35\}[/tex]
