(x-1)(x-3)(x+5)(x+7)=297
((x – 1)(x + 5))((x – 3)(x + 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 D = 16 + 128 > 0
Нет корней x1 = -8; x2 = 4
Ответ: x1=-8 , x2=4