5x^2 + 3x - 2 = 0 через формулу a(x-m)^2 + n = 0
5(x^2 + 3/5x) - 2 = 0
(x - m)^2 = x^2 - 2mx + m^2
5(x^2 + 2*x*3/10 + (3/10)^2 - (3/10)^2) - 2 = 0
5(x + 3/10)^2 - 5*9/100 - 2 = 0
5(x + 3/10)^2 - 2 9/20 = 0
m = - 3/10
n = - 2 9/20
A1 = b1 = 5
b3 = b1*q^2 = a1 + 3d
b5 = b1*q^4 = a1 + 15d
Подставляем
{ 5q^2 = 5 + 3d
{ 5q^4 = 5 + 15d
Выделяем 5
{ 5(q^2 - 1) = 3d
{ 5(q^4 - 1) = 15d
5(q^2 - 1)(q^2 + 1) = 5*3d
Подставляем 1 уравнение во 2 уравнение
3d*(q^2 + 1) = 5*3d
q^2 + 1 = 5
q^2 = 4
q1 = -2; q2 = 2
5*(4 - 1) = 3d
d = 5
Получаем: a1 = 5; d = 5
a4 = a1 + 3d = 5 + 5*3 = 20