Question

Найдите b1 и q если {b1+b3=30 ,b2+b4 =90

Answer 1

$\left \{ {{b1+b3=30} \atop {b2+b4=90}} \right.$⇒$\left \{ {{b1+b1q ^{2} =30} \atop {b1q+b1q^3=90}} \right.$
$\left \{ {{b1(1+q^2)=30} \atop {b1q(1+q^2)=90}} \right.$
1+q²=30/b₁;  ⇒b1·q·30/b1=90;  ⇒q=9/30=3;
b1=30/(1+q²)=30/(1+9)=30/10=3;