Đáp án:
\(x = y = - \frac{1}{2}\)
Giải thích các bước giải:
\(\begin{array}{l}
\left\{ \begin{array}{l}
{x^2} + y + \frac{1}{4} = 0\\
x + {y^2} + \frac{1}{4} = 0
\end{array} \right.\\
\to \left\{ \begin{array}{l}
{x^2} + y + \frac{1}{4} = x + {y^2} + \frac{1}{4}\\
x + {y^2} + \frac{1}{4} = 0
\end{array} \right.\\
\to \left\{ \begin{array}{l}
{x^2} - {y^2} - x + y = 0\\
x + {y^2} + \frac{1}{4} = 0
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\left( {x - y} \right)\left( {x + y} \right) - \left( {x - y} \right) = 0\\
x + {y^2} + \frac{1}{4} = 0
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\left( {x - y} \right)\left( {x - y - 1} \right) = 0\\
x + {y^2} + \frac{1}{4} = 0
\end{array} \right.\\
\to \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x = y\\
y + {y^2} + \frac{1}{4} = 0
\end{array} \right.\\
\left\{ \begin{array}{l}
x = y + 1\\
y + 1 + {y^2} + \frac{1}{4} = 0
\end{array} \right.
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = y = - \frac{1}{2}\\
\left\{ \begin{array}{l}
x = y + 1\\
y + {y^2} + \frac{5}{4} = 0\left( {vônghiệm} \right)
\end{array} \right.
\end{array} \right.\\
\to x = y = - \frac{1}{2}
\end{array}\)
