1) 3ax^2-2 (3a-2) x+3 (a-1) = 0 2) x (x-1) (x-2) (x-3) = 15 3) x^4-x^3-10x^2+2x+4=0

Найдем корни.

1) 3 * a * x^2 - 2 * (3 * a - 2) * x + 3 * (a - 1) = 0;

D = (-2 * (3 * a - 2)) ^2 - 4 * 3 * a * (3 * (a - 1)) = 4 * (9 * a^2 - 12 * a + 4) - 12 * a * (3 * a - 3) = 36 * a^2 - 36 * a + 16 - 36 * a^2 - 36 * a = 16 = 4^2;

x1 = (2 * (3 * a - 2) + 4) / (2 * 3 * a) = (6 * a - 4 + 4) / (6 * a) = 6 * a / (6 * a) = 1;

x2 = (6 * a - 4 - 4) / (6 * a) = (6 * a - 8) / (6 * a) = 1 - 4/3 * a.

2) x * (x - 1) * (x - 2) * (x - 3) = 15;

(x^2 - 3 * x) * (x^2 - 2 * x - 1 * x + 2) = 15;

(x^2 - 3 * x) * (x^2 - 3 * x + 2) = 15;

Пусть x^2 - 3 * x = a, тогда:

a * (a + 2) = 15;

a^2 + 2 * a - 15 = 0;

D = 4 - 4 * 1 * (-15) = 4 + 4 * 15 = 4 + 60 = 64 = 8^2;

x1 = (-2 + 8) / (2 * 1) = (-2 + 8) / 2 = 6/2 = 3;

x2 = (-2 - 8) / (2 * 1) = - 10/2 = - 5;

Ответ: х = 3 и х = - 5.

3) x^4 - x^3 - 10 * x^2 + 2 * x + 4 = 0;

Делим на x^2.

x^4/x^2 - x^3/x^2 - 10 * x^2/x^2 + 2 * x/x^2 + 4/x^2 = 0;

x^2 - x - 10 + 2/x + 4/x^2 = 0;

(x^2 + 4/x^2) - (x - 2/x) - 10 = 0;

Пусть (x - 2/x) = a.

(x - 2/x) ^2 = a^2;

x^2 - 2 * x * 2/x + 4/x^2 = a^2;

x^2 + 4/x^2 = a^2 + 4.

Тогда:

a^2 + 4 - a - 10 = 0;

a^2 - a - 6 = 0;

D = 1 - 4 * 1 * (-6) = 25;

a1 = (1 + 5) / 2 = 3;

a2 = (1 - 5) / 2 = - 2;

Получаем:

x - 2/x = 3;

x^2 - 3 * x - 2 = 0;

D = 9 - 4 * 1 * (-2) = 17;

x1 = (3 + √17) / 2;

x2 = (3 - √17) / 2;

x - 2/x = - 2;

x^2 + 2 * x - 2 = 0;

D = 4 - 4 * 1 * (-2) = 12;

x3 = (-2 + √12) / 2 = - 1 + √3;

x4 = (-2 - √12) / 2 = - 1 - √3.