(х² - 5х + 7)² - (х - 2)(х - 3) = 1
(x² - 5x + 7)² - (x² - 5x + 6) - 1 = 0
Пусть x² - 5x + 6 = t
(t + 1)² - t - 1 = 0
t² + 2t + 1 - t - 1 = 0
t² + t = 0
t ( t + 1) = 0
t1 = 0;
t2 = - 1
1) x² - 5x + 6 = 0
D = 25 - 24 = 1
x1 = ( 5 + 1)/2 = 6/2 = 3;
x2 = ( 5 - 1))/2 = 4/2 = 2;
2) x² - 5x + 6 = - 1
x² - 5x + 7 = 0
D = 25 - 28 < 0
Корней нет
Ответ
2; 3