Решите уравнение: х^4-2 х 3 - 3 х 2 + 4 х+4=0. Найдите сумму наибольшего и наименьшего корней уравнения.

х^4 - 2 х³ - 3 х² + 4 х + 4 = 0;

(x^4 - 2 x³) - (2 x² - 4 x) - (x² - 4) = 0;

x³ (x - 2) - 2 x (x - 2) - (x - 2) (x + 2) = 0;

(x - 2) (x³ - 2 x - x - 2) = 0;

(x - 2) [ (x³ - x) - (2 x + 2) ] = 0;

(x - 2) [x (x² - 1) - 2 (x + 1) ] = 0;

(x - 2) [x (x - 1) (x + 1) - 2 (x + 1) ] = 0;

(x - 2) [ (x + 1) (x (x - 1) - 2) ] = 0;

(x - 2) (x + 1) (x² - x - 2) = 0;

x² - x - 2 = 0;

D = 1 + 8 = 9;

x = (1 ± √9) : 2;

x = 2; x' = - 1;

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

(x - 2) ² (x + 1) ² = 0;

x - 2 = 0; x = 2;

x + 1 = 0; x' = - 1;

x + x' = 2 - 1 = 1.