Question

\(\left\{{}\begin{matrix}\frac{3}{x^2+y^2-1}+\frac{2y}{x}=1\\x^2+y^2+\frac{4x}{y}=22\end{matrix}\right.\)

Answer 1

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Đặt \(\left\{{}\begin{matrix}x^2+y^2-1=a\\\frac{x}{y}=b\end{matrix}\right.\) (1)

\(\Rightarrow\left\{{}\begin{matrix}\frac{3}{a}+\frac{2}{b}=1\\a+4b=21\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\frac{3}{a}+\frac{2}{b}=1\\a=21-4b\end{matrix}\right.\)

\(\Rightarrow\frac{3}{21-4b}+\frac{2}{b}=1\)

\(\Leftrightarrow2b^2-13b+21=0\)

\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}b=3\\a=9\end{matrix}\right.\\\left\{{}\begin{matrix}b=\frac{7}{2}\\a=7\end{matrix}\right.\end{matrix}\right.\) bạn tự thế vào (1) giải tiếp