2) (x-2)²(x²-4x)+3=0
(x²-4x-4)(x²-4x)+3 = 0
y = x²-4x
(y-4)y + 3 = 0
y² - 4y + 3 = 0
y1 = 3
y2 = 1
x²-4x = 3
x²-4x-3=0
x1 = 3
x2 = -1
x²-4x = 1
x²-4x-1=0
d1 = 4+1 = 5
x3 = 2+√5
x4 = 2-√5
ответ: 2-√5; -1; 3; 2+√5.
4) (x²-5x+2)(x²-5x-1) = 28
y = x²-5x
(y+2)(y-1) - 28 = 0
y² - y + 2y - 2 - 28 = 0
y² + y - 30 = 0
y1 = -6
y2 = 5
x²-5x = -6
x² - 5x + 6 = 0
x1 = 5
x²-5x = 5
x² - 5x - 5 = 0
d = 25 + 20 = 45 = (3√5)²
x3 = 2,5 + 1,5√5
x4 = 2,5 - 1,5√5
ответ: 2,5-1,5√5; -1; 5; 2,5+1,5√5.
2) (x-2)²(x²-4x)+3=0
(x²-4x-4)(x²-4x)+3 = 0
y = x²-4x
(y-4)y + 3 = 0
y² - 4y + 3 = 0
y1 = 3
y2 = 1
x²-4x = 3
x²-4x-3=0
x1 = 3
x2 = -1
x²-4x = 1
x²-4x-1=0
d1 = 4+1 = 5
x3 = 2+√5
x4 = 2-√5
ответ: 2-√5; -1; 3; 2+√5.
4) (x²-5x+2)(x²-5x-1) = 28
y = x²-5x
(y+2)(y-1) - 28 = 0
y² - y + 2y - 2 - 28 = 0
y² + y - 30 = 0
y1 = -6
y2 = 5
x²-5x = -6
x² - 5x + 6 = 0
x1 = 5
x2 = -1
x²-5x = 5
x² - 5x - 5 = 0
d = 25 + 20 = 45 = (3√5)²
x3 = 2,5 + 1,5√5
x4 = 2,5 - 1,5√5
ответ: 2,5-1,5√5; -1; 5; 2,5+1,5√5.