Решить уравнения высшей степени: 1) x^3+5x^2+7x+3=0 2) x^3+2x^2-4x+1=0 3) x^3-x^2-8x+12=0

1.
x³+5x²+7x+3 = 0
x³+x²+4x²+4x+3x+3 = 0
x²(x+1)+4x(x+1)+3(x+1) = 0
(x+1)(x²+4x+3) = (x+1)(x²+x+3x+3) = 0
(x+1)(x(x+1)+3(x+1)) = 0
(x+1)(x+1)(x+3) = 0
(x+1)²(x+3) = 0

x1=-1 (кратный корень), x2=-3

2.
x³+2x²-4x+1 = 0
x³-x²+3x²-3x-x+1 = 0
x²(x-1)+3x(x-1)-(x-1) = 0
(x-1)(x²+3x-1) = 0
x1=1
x²+3x-1 = 0
D=9+4=13
x2=(-3+√13)/2
x3=(-3-√13)/2

3.
x³-x²-8x+12 = 0
x³-2x²+x²-2x-6x+12 = 0
x²(x-2)+x(x-2)-6(x-2) = 0
(x-2)(x²+x-6) = 0
(x-2)(x²-2x+3x-6) = 0
(x-2)(x(x-2)+3(x-2)) = 0
(x-2)(x-2)(x+3) = 0
(x-2)²(x+3) = 0

x1=2 (кратный корень), x2=-3