Решите уравнение: (x+3y-2)^2+x^2-10xy+25y^2=0.

Ответ:

\[(x + 3y - 2)^{2} + (x - 5y)^{2} = 0\]

\[\left\{ \begin{matrix} x + 3y = 2 \\ x - 5y = 0 \\ \end{matrix} - \right.\ \text{\ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 8y = 2\ \ \ \ \ \ \ \ \\ x = 2 - 3y \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} y = \frac{1}{4} \\ x = \frac{5}{4} \\ \end{matrix} \right.\ \]

\[Ответ:\left( 1\frac{1}{4};\frac{1}{4} \right).\]