X (x-1) (x+1) (x-2) = -7/16

Найдем корни уравнения.

x * (x - 1) * (x + 1) * (x - 2) = - 7/16;

Сгруппируем многочлены и раскроем скобки.

(x * (x - 1)) * ((x + 1) * (x - 2)) = - 7/16;

Раскроем скобки.

(x * x - 1 * x) * (x * x - 2 * x + 1 * x - 2 * 1) = - 7/16;

(x² - x) * (x² - 2 * x + x - 2) = - 7/16;

(x² - x) * (x² - x - 2) = - 7/16;

Пусть x² - x = а, тогда получим:

a * (a - 2) = - 7/16;

a² - 2 * a + 7/16 = 0;

16 * a² - 32 * a + 7 = 0;

D = 1024 - 4 * 16 * 7 = 1024 - 448 = 576 = 24²;

a1 = (32 + 24) / 32 = 56/32 = 14/8 = 7/4;

a2 = (32 - 24) / 32 = 8/32 = 1/4;

Получаем:

1) x² - x = 7/4;

x² - x - 7/4 = 0;

4 * x² - 4 * x - 7 = 0;

D = 16 - 4 * 4 * (-7) = 128;

x1 = (4 + √128) / 8 = (1 + √8) / 2;

x2 = (4 - √128) / 8 = (1 - √8) / 2;

2) x² - x = 1/4;

x² - x - 1/4 = 0;

4 * x² - 4 * x - 1 = 0;

D = 16 - 4 * 4 * (-1) = 32;

x3 = (4 - √32) / 8 = (1 - √2) / 2;

x4 = (4 + √32) / 8 = (1 + √2) / 2.