2)
[tex]\it 0,2=\dfrac{\ 2^{(2}}{10}= \dfrac{1}{5}\\ \\ \\ 0,1(6)=\dfrac{16-1}{90}=\dfrac{\ 15^{(15}}{90}=\dfrac{1}{6}\\ \\ \\ \{a,\ \ b\}\ i.\ p.\ \{0,2;\ 0,1(6)\} \Rightarrow \{a,\ \ b\}\ i.\ p.\ \Big\{\dfrac{1}{5};\ \dfrac{1}{6}\Big\} \Rightarrow \\ \\ \\ \Rightarrow \{a,\ \ b\}\ d.\ p.\ \{5,\ \ 6\} \Rightarrow \dfrac{a}{5}=\dfrac{b}{6}=k \Rightarrow \begin{cases}\it a=5k\\ \\ \it b=6k\end{cases}\ \ \ \ \ \ (1)[/tex]
[tex]\it 2a+3b=56 \stackrel{(1)}{\Longrightarrow}\ 2\cdot5k+3\cdot6k=56 \Rightarrow10k+18k=56 \Rightarrow \\ \\ \\ \Rightarrow 28k=56|_{:28} \Rightarrow k=2\ \ \ \ \ \ (2)\\ \\ \\ (1),\ (2) \Rightarrow \begin{cases} \it a=5\cdot2=10\\ \\ \it b=6\cdot2=12\end{cases}[/tex]
