X (x - 3) (x - 1)(x - 2) = 15
(x^2 - 3x)(x^2 - 3x + 2) - 15 = 0
Пусть x^2 - 3x = t, тогда
t (t + 2) - 15 = 0
t^2 + 2t - 15 = 0
D = 4 + 4*15 = 64
t1 = ( - 2 + 8)/2 = 3;
t2 = ( - 2 - 8)/2 = - 5;
1) x^2 - 3x = 3
x^2 - 3x - 3 = 0
D = 9 + 12 = 21
x1 = ( 3 + √21)/2;
x2 = ( 3 - √21)/2;
2) x^2 - 3x = - 5
x^2 - 3x + 5 = 0
D = 9 - 4*5 = - 11 < 0
нет решений
Ответ
( 3 + √21)/2;
( 3 - √21)/2;