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

(x - 1) (x - 3) (х + 5) (х + 7) = 297

(х - 1) (x + 5)) ((х - 3) (х + 7)) = 297;

(x2 + 5x - x - 5) (x2 + 7x - 3x - 21) = 297;

(x2 + 4x - 5) (x2 + 4x - 21) = 297.

x2 + 4x = t, тогда:

(t - 5) (t - 21) = 297.

t2 - 21t - 5t + 105 = 297;

t2 - 26t - 192 = 0

t1 = - 6 и t2 = 32

x2 + 4x = - 6 или x2 + 4x = 32

x2 + 4x + 6 = 0 x2 + 4x - 32 = 0

D = 16 - 24 0

Нет корней x1 = - 8; x2 = 4

Ответ: x1 = - 8, x2 = 4