Đáp án:
139; 297
Giải thích các bước giải:
\(\begin{array}{l}
100a + 10b + c = 2\left( {10a + b + 10b + c + 10a + c} \right)\\
100a + 10b + c = 2\left( {20a + 11b + 2c} \right)\\
100a + 10b + c - 40a - 22b - 4c = 0\\
60a - 11b - 3c = 0\\
60a - 3c = 11b\\
\Rightarrow b\, \vdots \,3 \Rightarrow b \in \left\{ {0;3;6;9} \right\}\\
+ )b = 0 \Rightarrow 60a = 3c \Rightarrow c = 20a\, \Rightarrow c = 0;a = 0\left( L \right)\\
+ )\,b = 3 \Rightarrow 60a - 3c = 33 \Rightarrow 20a = c + 11\\
\Rightarrow c + 11\, \vdots \,20\,\,va\,\left( {c + 11} \right) \le 20\\
\Rightarrow a = 1;c = 9\\
+ )\,b = 6 \Rightarrow 60a - 3c = 66 \Rightarrow 20a = c + 22\\
\Rightarrow \left( {c + 22} \right)\, \vdots \,20\,va\,\,\left( {c + 22} \right) \le 31 \Rightarrow c + 22 = 20\left( L \right)\\
+ )\,b = 9 \Rightarrow 60a - 3c = 99 \Rightarrow 20a = c + 33\\
\Rightarrow \left( {c + 33} \right)\, \vdots \,20;\,33 \le c + 33 \le 42\\
\Rightarrow c + 33 = 40 \Rightarrow c = 7 \Rightarrow a = 2\\
Vay\,co\,hai\,so\,la\,139;\,297
\end{array}\)
