Question

дана геометрическая прогрессия
b1 + b2 = 20;
b2 + b3 = 45
****найти первые три числа

Answer 1

$\left \{ {{b_1+b_2=20} \atop {b_2+b_3=45}} \right.\; \; \left \{ {{b_1+b_1q=20} \atop {b_1q+b_1q^2=45}} \right.\; \; \left \{ {{b_1(1+q)=20} \atop {b_1q(1+q)=45}} \right.\; \; \left \{ {{1+q=\frac{20}{b_1}} \atop {1+q=\frac{45}{b_1q}}} \right.\\\\\frac{20}{b_1}=\frac{45}{b_1q}\; \; \Rightarrow \; \; \; 20\, b_1q=45\, b_1\; \; ,\; \; 20q=45\; \; ,\; \; q=\frac{45}{20}=\frac{9}{4}\\\\b_1=\frac{20}{1+q}=\frac{20}{1+\frac{9}{4}}=\frac{20\cdot 4}{4+9}=\frac{80}{13}\\\\b_2=b_1q=\frac{80}{13}\cdot \frac{9}{4}=\frac{180}{13}\\\\b_3=b_2q=\frac{180}{13}\cdot \frac{9}{4}=\frac{405}{13}$