\(\left\{{}\begin{matrix}u_1-u_3+u_5=65\\u_1+u_7=325\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}u_1-u_1.q^2+u_1.q^4=65\\u_1+u_1.q^6=325\end{matrix}\right.\)
\(\Rightarrow\dfrac{u_1-u_1.q^2+u_1.q^4}{u_1+u_1.q^6}=\dfrac{65}{325}=\dfrac{1}{5}\)
\(\Leftrightarrow\dfrac{1-a^2+q^4}{1+q^6}=\dfrac{1}{5}\Leftrightarrow q^6-5q^4+5q^2-4=0\)
Đặt \(q^2=a\ge0\Rightarrow a^3-5a^2+5a-4=0\Rightarrow a=4\)
\(\Rightarrow q^2=4\Rightarrow\left[{}\begin{matrix}q=2\\q=-2\end{matrix}\right.\) \(\Rightarrow u_1=\dfrac{325}{1+q^6}=5\)
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