\(\left(x+17\right)^{21}.\left(x-52\right)^{25}=0\)
\(\Rightarrow\orbr{\begin{cases}\left(x+17\right)^{21}=0\\\left(x-52\right)^{25}=0\end{cases}}\Rightarrow\orbr{\begin{cases}x+17=0\\x-52=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=-17\\x=52\end{cases}}\)
vậy \(\orbr{\begin{cases}x=-17\\x=52\end{cases}}\)