(x - 3)(x - 5)(x - 4)^2 - 12 = 0
(x^2 - 8x + 15)(x^2 - 8x + 16) - 12 = 0
Пусть t = x^2 - 8x + 15, тогда
t (t + 1) - 12 = 0
t^2 + t - 12 = 0
D = 1 + 48 = 49
t1 = ( - 1 + 7)/2 = 6/2 = 3
t2 = ( - 1 - 7)/2 = - 8/2 = - 4
Обратная заменя
x^2 - 8x + 15 = 3
x^2 - 8x + 12 = 0
D = 64 - 48 = 16
x1 = ( 8 + 4)/2 = 12/2 = 6
x2 = (8 - 4)/2 = 4/2 = 2
x^2 - 8x + 15 = - 4
x^2 - 8x + 19 = 0
D = 64 - 76 = - 12
Нет решений
Ответ
2; 6