Question

giải giúp mình câu này với

\(\left\{{}\begin{matrix}x+y=5\\x^4+y^4=97\end{matrix}\right.\)

cảm ơn trước :)

Answer 1

Xét :\(x^4+y^4=\left(x^2+y^2\right)^2-2x^2y^2=\left[\left(x+y\right)^2-2xy\right]^2-2x^2y^2\)

\(97=\left(25-2xy\right)^2-2x^2y^2\)

\(2x^2y^2-100xy+528=0\)

\(\Leftrightarrow\left(xy-6\right)\left(xy-44\right)=0\)\(\Rightarrow\left[{}\begin{matrix}xy=6\\xy=44\end{matrix}\right.\)

TH1:\(\left\{{}\begin{matrix}x+y=5\\xy=6\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=2\\y=3\end{matrix}\right.\\\left\{{}\begin{matrix}x=3\\y=2\end{matrix}\right.\end{matrix}\right.\)

TH2:\(\left\{{}\begin{matrix}x+y=5\\xy=44\end{matrix}\right.\)(vô nghiệm)