Решить Уравнение: 3x³-4x²-5x+2=0

3x^3 - 4x^2 - 5x + 2 = 0;

(3x^3 - 4x^2 - 4x) - (x-2) = 0;

x (3x^2 - 4x - 4) - (x-2) = 0;

3x^2 - 4x - 4 = 0;

D = 16 + 48 = 64;

x1 = 2; x2 = - 4/3;

3x^2 - 4x - 4 = 3 (x-2) (x + 4/3) = (x-2) (3x+4) ;

x (3x^2 - 4x - 4) - (x-2) = 0;

x (x-2) (3x+4) - (x-2) = 0;

(x-2) (x (3x+4) - 1) = 0;

(x-2) (3x^2 + 4x - 1) = 0;

x - 2=0; x = 2;

4x^2 + 4x - 1 = 0;

D = 16 + 16 = 32 = (4sgrt2) ^2;

x = (-1+sgrt2) / 2; x2 = (-1 - sgrt2) / 2.