Đáp án:
$\left( {x;y} \right) = \left( {2;4} \right)$
Giải thích các bước giải:
Ta có:
$\begin{array}{l}
2xy + 4x + 3y - 36 = 0\\
\Leftrightarrow \left( {2xy + 3y} \right) + 4x - 36 = 0\\
\Leftrightarrow y\left( {2x + 3} \right) + 2\left( {2x + 3} \right) - 42 = 0\\
\Leftrightarrow \left( {y + 2} \right)\left( {2x + 3} \right) = 42\left( 1 \right)
\end{array}$
Mà
$\begin{array}{l}
x,y \in N*\\
\left\{ \begin{array}{l}
y + 2 > 2\\
2x + 3 > 5;2x + 3\not \vdots 2
\end{array} \right.
\end{array}$
$\left( 1 \right) \Leftrightarrow \left\{ \begin{array}{l}
y + 2 = 6\\
2x + 3 = 7
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
y = 4\\
x = 2
\end{array} \right.$
Vậy $\left( {x;y} \right) = \left( {2;4} \right)$
