Ответ:
Имеем три члена геометрической прогрессии.
bn = b1 * q^(n — 1);
b2 = b1 * q;
b3 = b1 * q^2;
b1 + b1 * q + b1 * q^2 = 14;
b1 * (1 + q + q^2) = 14;
b1 * q^2 + 5 — b1 * q — 11 = b1 * q + 11 — b1 + 15;
b1 * q^2 — 2 * b1 * q + b1 = 32;
b1 * (q^2 — 2 * q + 1) = 32;
32/(q^2 — 2 * q + 1) = 14/(q^2 + q + 1);
32 * (q^2 + q + 1) = 14 * (q^2 — 2 * q + 1);
32 * q^2 + 32 * q + 32 — 14 * q^2 + 28 * q — 14 = 0;
18 * q^2 + 60 * q + 18 = 0;
3 * q^2 + 10 * q + 3 = 0;
D = 100 — 4 * 9 = 64;
q1 = (-10 — 8)/6 = -3;
q2 = (-10 + 8)/6 = -1/3;
1) b1 = 14/(9 — 3 + 1) = 2;
b2 = -6;
b3 = 18;
2) b1 = 14/(7/9) = 14 * 9/7 = 18;
b2 = -6;
b3 = 2.