Question

aflati cifrele a si b , a < b , care verifica egalitatea ( a, ba + b, ab) : 3,7 = 1,5

Answer 1

a,ba+b,ab=3,7·1,5
⇒a,ba+b,ab=5,55
⇒a<b⇒a+b=5 sau b+a=5⇒a,b∈[1,4][2,3];

Answer 2

 [tex](\overline{a,ba}+\overline{b,ab}):3,7=1,5\;\Leftrightarrow\;\overline{a,ba}+\overline{b,ab}=1,5\cdot3,7=5,55\;\\ \frac{\overline{aba}}{100}+\frac{\overline{bab}}{100}=5,55\;\rightarrow\;100a+10b+a+100b+10a+b=555\\ 111a+111b=555 \;\;|_{:111}\;\rightarrow\;\fbox{a+b=5}\\ ptr. a\ \textless \ b\; \Rightarrow\; (a;b)\,=\,\{(1;4)\;;\;(2;3)\,\}[/tex]