(x^2-2x-5)^2-2(x^2-2x-3)-4=0

(х - 2х - 5) - 2(х - 2х - 3) - 4 = 0.

Введем новейшую переменную х - 2х = у.

(у - 5) - 2(у - 3) - 4 = 0;

у - 10у + 25 - 2у + 6 - 4 = 0;

у - 12у + 27 = 0;

D = b - 4ac;

D = (-12) - 4 * 1 * 27 = 144 - 108 = 36;

x = (-b D)/(2a);

x = (-(-12) 36)/(2 * 1) = (12 6)/2.

y1 = (12 + 6)/2 = 18/2 = 9;

y2 = (12 - 6)/2 = 6/2 = 3.

Выполним оборотную подстановку.

1) х - 2х = 9;

х - 2х - 9 = 0;

D = (-2) - 4 * 1 * (-9) = 4 + 36 = 40;

x = (-(-2) 40)/(2 * 1) = (2 210)/2 = 1 10;

x1 = 1 + 10;

x2 = 1 - 10.

2) x - 2x = 3;

x - 2x - 3 = 0;

D = (-2) - 4 * 1 * (-3) = 4 + 12 = 16;

x = (-(-2) 16)/(2 * 1) = (2 4)/2;

x1 = (2 + 4)/2 = 6/2 = 3;

x2 = (2 - 4)/2 = -2/2 = -1.

Ответ. 1 + 10; 1 - 10; 3; -1.