\[\boxed{\text{708\ (708).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ a_{2} \cdot a_{6} = a_{3} \cdot a_{5};\]
\[a_{2} \cdot a_{6} = a_{1}q \cdot a_{1}q^{5} = a_{1}^{2} \cdot q^{6},\]
\[a_{3} \cdot a_{5} = a_{1}q² \cdot a_{1}q^{4} = a_{1}^{2}{\cdot q}^{6},\]
\[a_{2} \cdot a_{6} = a_{3} \cdot a_{5} \Longrightarrow ч.т.д.\]
\[\textbf{б)}\ a_{n - 3} \cdot a_{n + 8} = a_{n} \cdot a_{n + 5},\]
\[где\ n > 3,\]
\[\ a_{n - 3} \cdot a_{n + 8} = a_{1}q^{n - 4} \cdot a_{1}q^{n + 7} =\]
\[= a_{1}^{2}q^{2n + 3},\]
\[a_{n} \cdot a_{n + 5} = a_{1}q^{n - 1} \cdot a_{1}q^{n + 4} =\]
\[= a_{1}^{2}q^{2n + 3},\]
\[a_{n - 3} \cdot a_{n + 8} = a_{n} \cdot a_{n + 5} \Longrightarrow ч.т.д.\]