Найдите действительные решения уравнения: (x-1) (x-3) (x+5) (x+7) = 297

1. Преобразуем:

(x - 1) (x - 3) (x + 5) (x + 7) = 297; (x + 2 - 5) (x + 2 - 3) (x + 2 + 3) (x + 2 + 5) = 297; ((x + 2) ^2 - 5^2) ((x + 2) ^2 - 3^2) = 297; ((x + 2) ^2 - 25) ((x + 2) ^2 - 9) = 297; ((x + 2) ^2 - 17 - 8) ((x + 2) ^2 - 17 + 8) = 297; ((x + 2) ^2 - 17) ^2 - 8^2 = 297; ((x + 2) ^2 - 17) ^2 - 64 = 297; ((x + 2) ^2 - 17) ^2 = 297 + 64; ((x + 2) ^2 - 17) ^2 = 361; ((x + 2) ^2 - 17) ^2 = 19^2; (x + 2) ^2 - 17 = ±19; (x + 2) ^2 = 17 ± 19.

2. (x + 2) ^2 = 17 - 19 = - 2 < 0 - нет решений;

3. (x + 2) ^2 = 17 + 19;

(x + 2) ^2 = 36; x + 2 = ±6; x = - 2 ± 6; x1 = - 2 - 6 = - 8; x2 = - 2 + 6 = 4.

Ответ: - 8; 4.