Đáp án:
\[\left\{ \begin{array}{l}
x = 3\\
y = \frac{7}{2}
\end{array} \right.\]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
13{x^2} + 6x + 16{y^2} - 24xy - 40y + 61 = 0\\
\Leftrightarrow \left( {9{x^2} + 16{y^2} + 25 - 24xy - 40y + 30x} \right) + \left( {4{x^2} - 24x + 36} \right) = 0\\
\Leftrightarrow \left[ {{{\left( {3x} \right)}^2} + {{\left( {4y} \right)}^2} + {5^2} - 2.3x.4y - 2.4y.5 + 2.3x.5} \right] + 4\left( {{x^2} - 6x + 9} \right) = 0\\
\Leftrightarrow {\left( {3x - 4y + 5} \right)^2} + 4.{\left( {x - 3} \right)^2} = 0\\
\Leftrightarrow \left\{ \begin{array}{l}
3x - 4y + 5 = 0\\
x - 3 = 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x = 3\\
y = \frac{7}{2}
\end{array} \right.
\end{array}\)
