Đáp án:
\(\,\left( {x;\,\,y} \right) = \left( {\frac{1}{4};\,\,\frac{1}{4}} \right)\)
Giải thích các bước giải:
\[\begin{array}{l}
\left| {x + 3y - 1} \right| + {\left( {2y - \frac{1}{2}} \right)^{2000}} = 0\,\,\,\left( * \right)\\
Vi\,\,\left\{ \begin{array}{l}
\left| {x + 3y - 1} \right| \ge 0\,\,\,\forall x,\,\,y\\
{\left( {2y - \frac{1}{2}} \right)^{2000}} \ge 0\,\,\,\forall y
\end{array} \right.\\
\Leftrightarrow \left( * \right) \Leftrightarrow \left\{ \begin{array}{l}
\left| {x + 3y - 1} \right| = 0\\
{\left( {2y - \frac{1}{2}} \right)^{2000}} = 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x + 3y - 1 = 0\\
2y - \frac{1}{2} = 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x = - 3y + 1\\
y = \frac{1}{4}
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x = - \frac{3}{4} + 1 = \frac{1}{4}\\
y = \frac{1}{4}
\end{array} \right..\\
Vay\,\,\,\left( {x;\,\,y} \right) = \left( {\frac{1}{4};\,\,\frac{1}{4}} \right).
\end{array}\]
