\(\Leftrightarrow\left\{{}\begin{matrix}1=x^5+y^5\\x^9+y^9=x^4+y^4\end{matrix}\right.\)
\(\Rightarrow x^9+y^9=\left(x^4+y^4\right)\left(x^5+y^5\right)\)
\(\Leftrightarrow x^4y^5+x^5y^4=0\)
\(\Leftrightarrow x^4y^4\left(x+y\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\y=0\\x=-y\end{matrix}\right.\)
Thế vào pt đầu ...