Question

aflați a,b,c știind ca (a+b+c)×ac(cu bara)=234 va rog am nevoie de ajutor

Answer 1

   
[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]