Задание 1. Ввести вспомогательное неизвестное и решить уравнение: (3x^2-x-4)(3x^2-x+2)-7=0

1) (3x^2 - x - 4)(3x^2 - x + 2) - 7 = 0
Подмена 3x^2 - x = y
(y - 4)(y + 2) - 7 = 0
y^2 - 4y + 2y - 8 - 7 = y^2 - 2y - 15 = 0
(y - 5)(y + 3) = 0
а) y - 5 = 3x^2 - x - 5 = 0
D = 1 - 4*3(-5) = 1 + 60 = 61
x1 = (1 - 61)/6; x2 = (1 + 61)/6
б) y + 3 = 3x^2 - x + 3 = 0
D = 1 - 4*3*3 = 1 - 36 = -35 lt; 0
Корней нет.
Ответ: x1 = (1 - 61)/6; x2 = (1 + 61)/6

2) (x^2 - 3x + 2)(x^2 - 7x + 12) = 4
(x - 1)(x - 2)(x - 3)(x - 4) = 4
(x - 1)(x - 4)*(x - 2)(x - 3) = 4
(x^2 - 5x + 4)(x^2 - 5x + 6) = 4
Подмена x^2 - 5x + 4 = y
y(y + 2) = 4
y^2 + 2y - 4 = 0
D = 4 - 4*1(-4) = 4 + 16 = 20 = (25)^2
а) y1 = x^2 - 5x + 4 = (-2 - 25)/2 = -1 - 5
x^2 - 5x + 5 + 5 = 0
D = 25 - 4*(5 + 5) = 5 - 45 lt; 0
Корней нет
б) y2 = x^2 - 5x + 4 = -1 + 5
x^2 - 5x + 5 - 5 = 0
D = 25 - 4(5 - 5) = 5 + 45
x1 = (5 - (5 + 45))/2; x2 = (5 + (5 + 45))/2