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