Question

\(\left\{{}\begin{matrix}x^2+y^2=5\\x^4+y^4+6x^2y^2+20xy=81\end{matrix}\right.\)

Answer 1

\(x^4+y^4+6x^2y^2+20xy=81\)

\(\Leftrightarrow\left(x^2+y^2\right)^2+4x^2y^2+20xy=81\)

\(\Leftrightarrow25+4x^2y^2+20xy=81\)

\(\Leftrightarrow4\left(xy\right)^2+20xy-56=0\Rightarrow\left[{}\begin{matrix}xy=2\\xy=-7\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}y=\frac{2}{x}\\y=-\frac{7}{x}\end{matrix}\right.\)

Thế vào pt đầu:

\(\left[{}\begin{matrix}x^2+\frac{4}{x^2}=5\\x^2+\frac{49}{x^2}=5\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x^4-5x^2+4=0\\x^4-5x^2+49=0\end{matrix}\right.\) \(\Leftrightarrow...\)