\(\left\{{}\begin{matrix}u_1+u_7=26\\u_2^2+u_6^2=466\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}u_1+u_1+6d=26\\\left(u_1+d\right)^2+\left(u_1+5d\right)^2=466\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}u_1=13-3d\\\left(13-3d+d\right)^2+\left(13-3d+5d\right)^2=466\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}u_1=13-3d\\\left(13-2d\right)^2+\left(13+2d\right)^2=466\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}u_1=13-3d\\8d^2+388=466\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}u_1=13-3d\\d^2=16\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}u_1=13-3d\\d=4\left(ktm\right)\cup d=-4\left(tm\right)\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}u_1=25\\d=-4\end{matrix}\right.\)
\(S_{20}=\dfrac{20}{2}.\left[2.25+19.\left(-4\right)\right]=-260\)
