Разликата на аритметичната прогресия

[emil3993]

[tex]\begin{array}{|l} 2a_{1 } +14d= 30 \\ a_{1 }^{2}.45d = 209 \end{array}[/tex]
a7+a9=30
a6+a10=30
Какво да правя по-натам. Зацепих.Отговор:б

[Добромир Глухаров]

$\begin{array}{|l}a_7+a_9=30\\a_6.a_{10}=209\end{array}\Leftrightarrow\begin{array}{|l}a_8-d+a_8+d=30\\(a_8-2d).(a_8+2d)=209\end{array}\Leftrightarrow\begin{array}{|l}2a_8=30\\a_8^2-4d^2=209\end{array}\Leftrightarrow\\\begin{array}{|l}a_8=15\\15^2-4d^2=209\end{array}\Rightarrow 4d^2=15^2-209=225-209=16\Rightarrow d^2=4$

[emil3993]

$\begin{array}{|l}a_7+a_9=30\\a_6.a_{10}=209\end{array}\Leftrightarrow\begin{array}{|l}a_8-d+a_8+d=30\\(a_8-2d).(a_8+2d)=209\end{array}\Leftrightarrow\begin{array}{|l}2a_8=30\\a_8^2-4d^2=209\end{array}\Leftrightarrow\\\begin{array}{|l}a_8=15\\15^2-4d^2=209\end{array}\Rightarrow 4d^2=15^2-209=225-209=16\Rightarrow d^2=4$

Благодаря, за това не се сетих.