[tex]\bf\\
(a+b+c)\times \overline{ac}=234\\\\
\texttt{Descompunem numarul 234 in factori primi:}\\\\
234 = 2 \times 3^2 \times 13 \\\\
\texttt{Varianta 1:}\\
\overline{ac}=13\\
\Longrightarrow~~a = 1~~\texttt{si}~~c = 3\\
\Longrightarrow~~(1 + b +3)\times 13 = 234\\
1+b+3 = 2 \times 3^2 = 2 \times 9 = 18~~~ \text{conform descompunerii}\\
b = 18 -1-3 = 14~~\text{Solutie respinsa deoarece a, b, c sunt cifre.}
[/tex]
[tex]\bf\\
\texttt{Varianta 2:}\\
\overline{ac}=2 \times 13 = 26~~~\texttt{din descompunere}\\
\Longrightarrow~~a = 2~~\texttt{si}~~c = 6\\
\Longrightarrow~~(2 + b +6)\times 26 = 234\\
2+b+6 = 3^2 = 9 ~~~ \texttt{conform descompunerii}\\
b = 9 -2-6 = 1\\\\
\Longrightarrow~~\boxed{\bf (2 + 1 +6)\times 26 = 234}\\\\
\Longrightarrow~~\texttt{Solutia: }~~\boxed{\bf a=2;~b=1; c=6 }[/tex]
