Đáp án:
\[x = 7;y = 5\]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
900:\left( {x + y} \right) = \overline {xy} \\
\Leftrightarrow 900 = \left( {x + y} \right)\overline {xy} \\
900 = {2^2}{.3^2}{.5^2}\\
\left. \begin{array}{l}
0 < x \le 9;\,\,0 \le y \le 9 \Rightarrow 0 < x + y \le 18\\
\overline {xy} < 100 \Rightarrow x + y > 9
\end{array} \right\} \Rightarrow 9 < x + y \le 18\\
TH1:\,\,x + y = {2^2}.3 = 12 \Rightarrow \overline {xy} = 75\,\,\,\left( {t/m} \right)\\
TH2:x + y = 2.5 = 10 \Rightarrow \overrightarrow {xy} = 90\,\,\,\left( L \right)\\
TH3:\,\,x + y = {2.3^2} = 18 \Rightarrow \overline {xy} = 50\,\,\,\left( L \right)
\end{array}\)
Vậy \(x = 7;y = 5\)
