Найдите знаменатель геометрической прогрессии если c6 = 25, c8= 4 С решением .

[latex]c_{6}=c_{1}*q^5\\c_{8}=c_{1}*q^7\\\\ \left \{ {{25=c_{1}*q^5} \atop {4=c_{1}*q^7}} \right. =\ \textgreater \ Razdelim-2yr-na-1=\ \textgreater \ \\\\=\ \textgreater \ \left \{ {{25=c_{1}*q^5} \atop {\frac{4}{25}=q^2}} \right.\left \{ {{25=c_{1}*q^5} \atop {+-\frac{2}{5}=q}} \right.\\\\Ordelno-reshaem-pervoe-yravnenie\\1)25=c_{1}*(\frac{2}{5})^5\\\\25=c_{1}*\frac{32}{3125}\\\\c_{1}=\frac{25}{\frac{32}{3125}}\\\\c_{1}=\frac{25*3125}{32}\\\\c_{1}=\frac{78125}{32}\\\\c_{1}=2441\frac{13}{32}[/latex] [latex]2)25=c_{1}*(\frac{-2}{5})^5\\\\25=c_{1}*(-\frac{32}{3125})\\\\c_{1}=\frac{25}{\frac{-32}{3125}}\\\\c_{1}=\frac{25*3125}{-32}\\\\c_{1}=-\frac{78125}{32}\\\\c_{1}=-2441\frac{13}{32}[/latex] Вернемся в систему, и получим две пары решений [latex]1. \left \{ {{c_1}=2441\frac{13}{32}Ї} \atop {q=\frac{2}{5}}} \right. 2. \left \{ {{c_1}=-2441\frac{13}{32}Ї} \atop {q=-\frac{2}{5}}} \right. [/latex]x] Ответ: знаменатель прогрессии равен +-2/5