Notăm cele două numere cu a și b.
[tex]\it m_a=\dfrac{a+b}{2}=40 \Rightarrow a+b=80\ \ \ \ \ (*)\\ \\ \\ 0,2=\dfrac{\ 2^{(2}}{10}=\dfrac{1}{5};\ \ \ 0,(3)=\dfrac{\ 3^{(3}}{9}=\dfrac{1}{3}\\ \\ \\ \{a,\ \ b\}\ i.\ p.\ \Big\{\dfrac{1}{5},\ \ \dfrac{1}{3}\Big\} \Rightarrow \{a,\ \ b\}\ d,\ p.\ \{5,\ \ 3\} \Rightarrow \dfrac{a}{5}=\dfrac{b}{3}=\\ \\ \\ =\dfrac{a+b}{5+3}\ \stackrel{(*)}{=}\ \dfrac{80}{8}=10 \Rightarrow \begin{cases} \it a=5\cdot10=50\\ \\ \it b=3\cdot10=30\end{cases}[/tex]
