Đặt \(\left\{{}\begin{matrix}x+5=a\\x-4=b\end{matrix}\right.\)
\(\Rightarrow a^4+b^4=\left(a+b\right)^4\)
\(\Leftrightarrow a^4+b^4=a^4+b^4+4a^3b+6a^2b^2+4ab^3\)
\(\Leftrightarrow2a^3b+3a^2b^2+2ab^2=0\)
\(\Leftrightarrow ab\left(2a^2+2ab+2b^2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}ab=0\\2\left(a+\frac{3b}{4}\right)^2+\frac{7b^2}{8}=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}a=0\\b=0\\a=b=0\left(vn\right)\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x+5=0\\x-4=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=4\\x=-5\end{matrix}\right.\)
