Đáp án:
\(\left\{ \begin{array}{l}
x = \frac{{\sqrt 5 + 1 + \sqrt 3 }}{3}\\
y = \frac{{\sqrt 5 - 1 + \sqrt 3 }}{3}
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
\left\{ \begin{array}{l}
x\sqrt 5 - \left( {1 + \sqrt 3 } \right)y = \left( {1 - \sqrt 3 } \right)x + y\sqrt 5 \\
x\sqrt 5 - \left( {1 + \sqrt 3 } \right)y = 1
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\left( {\sqrt 5 - 1 + \sqrt 3 } \right)x = \left( {\sqrt 5 + 1 + \sqrt 3 } \right)y\\
x\sqrt 5 - \left( {1 + \sqrt 3 } \right)y = 1
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \frac{{\sqrt 5 + 1 + \sqrt 3 }}{{\sqrt 5 - 1 + \sqrt 3 }}y\\
x\sqrt 5 - \left( {1 + \sqrt 3 } \right)y = 1
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \frac{{\sqrt 5 + 1 + \sqrt 3 }}{{\sqrt 5 - 1 + \sqrt 3 }}y\\
\frac{{\sqrt 5 + 1 + \sqrt 3 }}{{\sqrt 5 - 1 + \sqrt 3 }}y.\sqrt 5 - \left( {1 + \sqrt 3 } \right)y = 1\left( * \right)
\end{array} \right.\\
\left( * \right) \to y\left( {\frac{{\sqrt 5 + 1 + \sqrt 3 }}{{\sqrt 5 - 1 + \sqrt 3 }}.\sqrt 5 - 1 - \sqrt 3 } \right) = 1\\
\to y.\left( {\frac{{5 + \sqrt 5 + \sqrt {15} - \sqrt 5 + 1 - \sqrt 3 - \sqrt {15} + \sqrt 3 - 3}}{{\sqrt 5 - 1 + \sqrt 3 }}} \right) = 1\\
\to y\left( {\frac{3}{{\sqrt 5 - 1 + \sqrt 3 }}} \right) = 1\\
\to y = \frac{{\sqrt 5 - 1 + \sqrt 3 }}{3}\\
\to x = \frac{{\sqrt 5 + 1 + \sqrt 3 }}{{\sqrt 5 - 1 + \sqrt 3 }}.\frac{{\sqrt 5 - 1 + \sqrt 3 }}{3} = \frac{{\sqrt 5 + 1 + \sqrt 3 }}{3}
\end{array}\)
