ЖЕДАЛЙАШОВАПРЫГНРМ ВППЦКП
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b2 = b1*q;
b3 = b1*q^2
Числа b1, b2+2, b3 - это арифметическая прогрессия с разностью d..
b2 + 2 = b1*q + 2 = b1 + d
b3 = b1*q^2 = b1 + 2d
Числа b1, b2+2, b3+9 - это геометрическая прогрессия со знам. p.
b2 + 2 = b1*q + 2 = b1*p
b3 + 9 = b1*q^2 + 9 = b1*p^2
Составляем систему
{ b1*q + 2 = b1 + d
{ b1*q^2 = b1 + 2d
{ b1*q + 2 = b1*p
{ b1*q^2 + 9 = b1*p^2
Преобразуем
{ b1*(q - 1) = d - 2
{ b1*(q^2 - 1) = b1*(q - 1)(q + 1) = 2d
{ b1*(p - q) = 2
{ b1*(p^2 - q^2) = b1*(p - q)(p + q) = 9
Получаем
{ b1*(q - 1) = d - 2
{ q + 1 = 2d/(d - 2)
{ b1*(p - q) = 2
{ p + q = 9/2 = 4,5
Подставляем q из 2 уравнения в 1.
{ q = 2d/(d-2) - 1 = (2d-d+2)/(d-2) = (d+2)/(d-2) = 1 + 4/(d-2)
{ b1*4/(d-2) = d - 2;
Получаем
b1 = (d-2)^2 / 4
Подставляем p из 4 уравнения в 3
{ b1 = 2/(p - q)
{ p + q = 4,5
Получаем p = 4,5 - q; p - q = 4,5 - 2q
q = 1 + 4/(d-2) = (d-2+4)/(d-2) = (d+2)/(d-2);
p - q = 4,5 - 2(d+2)/(d-2) = 9/2 - (2d+4)/(d-2)
p - q = (9d-18-4d-8)/(2d-4) = (5d-26)/(2d-4)
b1 = 2/(p - q) = 2*(2d-4)/(5d-26) = (4d-8)/(5d-26)
Приравниваем b1
(d-2)^2 / 4 = (4d-8) / (5d-26) = 4(d-2) / (5d-26)
Делим на (d-2)
(d-2) / 4 = 4 / (5d-26)
(d-2)(5d-26) = 16
5d^2 - 10d - 26d + 52 - 16 = 0
5d^2 - 36d + 36 = 0
D/4 = (b/2)^2 - ac = (-18)^2 - 5*36 = 324 - 180 = 144 = 12^2
d1 = (b/2 - √(D/4))/a = (18 - 12)/5 = 6/5
d2 = (b/2 + √(D/4))/a = (18 + 12)/5 = 6
Находим все остальное.
1) d1 = 6/5; b1 = (d-2)^2 / 4 = (6/5 - 2)^2 / 4 = (-4/5)^2 / 4 = (16/25) / 4 = 4/25
q = (d+2)/(d-2) = (6/5 + 2) / (6/5 - 2) = (16/5) / (-4/5) = 16/(-4) = -4
p = 4,5 - q = 4,5 + 4 = 8,5 = 17/2
b2 = b1*q = 4/25*(-4) = -16/25; b2 + 2 = 2 - 16/25 = 34/25
b3 = b2*q = (-16/25)*(-4) = 64/25; b3 + 9 = 9+64/25 = 289/25
Проверяем
b1, b2, b3 = 4/25; -16/25; 64/25 - геом. прогрессия с q = -4
b1, b2+2, b3 = 4/25; 34/25; 64/25 - ариф. прогрессия с d = 30/25 = 6/5
b1, b2+2, b3+9 = 4/25; 34/25; 289/25 - геом. прогрессия с p = 17/2
2) d2 = 6; b1 = (d-2)^2 / 4 = (6-2)^2 / 4 = 4^2 / 4 = 4
q = (d+2)/(d-2) = (6+2)/(6-2) = 8/4 = 2
p = 4,5 - q = 4,5 - 2 = 2,5 = 5/2
b2 = b1*q = 4*2 = 8; b2 + 2 = 10
b3 = b2*q = 8*2 = 16; b3 + 9 = 25
Проверяем
b1, b2, b3 = 4; 8; 16 - геом. прогрессия с q = 2
b1, b2+2, b3 = 4; 10; 16 - ариф. прогрессия с d = 6
b1; b2+2; b3+9 = 4; 10; 25 - геом. прогрессия с p = 5/2