\(\left\{{}\begin{matrix}u_1+u_3=10\\\left(u_1+u_3\right)^2-2u_1u_3=50\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}u_1+u_3=10\\u_1u_3=25\end{matrix}\right.\)
Theo Viet đảo, \(u_1\) và \(u_3\) là nghiệm:
\(x^2-10x+25=0\Rightarrow x=5\)
\(\Rightarrow u_1=u_3=5\)
\(\Rightarrow\left\{{}\begin{matrix}u_1=5\\u_1q^2=5\end{matrix}\right.\) \(\Rightarrow q^2=1\Rightarrow q=\pm1\)