Đáp án:
\(\left\{ \begin{array}{l}
x = \dfrac{{21 - 2\sqrt 7 }}{{3\sqrt 5 - 6}}\\
y = \dfrac{{45 - 6\sqrt 7 + 9\sqrt 5 }}{{2\left( {3\sqrt 5 - 6} \right)}}
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
\left\{ \begin{array}{l}
3\sqrt 5 x - 4y = 15 - 2\sqrt 7 \\
3x - 2y = - 3
\end{array} \right.\\
\to \left\{ \begin{array}{l}
3\sqrt 5 x - 4y = 15 - 2\sqrt 7 \\
- 6x + 4y = 6
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\left( {3\sqrt 5 - 6} \right)x = 21 - 2\sqrt 7 \\
3x - 2y = - 3
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{{21 - 2\sqrt 7 }}{{3\sqrt 5 - 6}}\\
y = \dfrac{{3x + 3}}{2} = \dfrac{{3.\dfrac{{21 - 2\sqrt 7 }}{{3\sqrt 5 - 6}} + 3}}{2} = \dfrac{{63 - 6\sqrt 7 + 9\sqrt 5 - 18}}{{2\left( {3\sqrt 5 - 6} \right)}}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{{21 - 2\sqrt 7 }}{{3\sqrt 5 - 6}}\\
y = \dfrac{{45 - 6\sqrt 7 + 9\sqrt 5 }}{{2\left( {3\sqrt 5 - 6} \right)}}
\end{array} \right.
\end{array}\)
