[tex]\it Vom\ nota\ cele\ trei\ numere\ cu\ a,\ b,\ c.\\ \\ \{a,\ b,\ c\}\ d.\ p.\ \{5,\ 7,\ 12\} \Rightarrow \dfrac{a}{5} = \dfrac{b}{7}= \dfrac{c}{12} \ \ \ \ (1)[/tex]
[tex]\it (1) \Rightarrow c>b>a\\ \\ c-a=49\ \ \ \ \ (2)\\ \\ \dfrac{c}{12}= \dfrac{a}{5}= \dfrac{c-a}{12-5}\ \stackrel{(2)}{=}\ \dfrac{49}{7}=7 \Rightarrow \begin{cases}\it c=12\cdot7=84\\ \\ \it a=5\cdot7=35 \end{cases} \\ \\ a=35\ \stackrel{(1)}{\Longrightarrow} \dfrac{35}{5}= \dfrac{b}{7} \Rightarrow\ 7= \dfrac{b}{7}\ \Rightarrow\ b=7\cdot7=49[/tex]
[tex]\it\ Deci:\ \ a=35,\ \ b=49,\ \ c=84[/tex]
