Question

(x^2-5x-7)^2-(x-3)*(x-2)=25

Answer 1

(x^2 - 5x - 7)^2 - (x^2 - 5x + 6) = 25
Пусть  x^2 - 5x = t, тогда
(t - 7)^2 - (t + 6) = 25
t^2 - 14t + 49 - t - 6 - 25 = 0
t^2 - 15t + 18 = 0
D = 153
t1 = (15 + 3√17)/2
t2 = (15 - 3√17)/2

Обратная замена
x^2 - 5x = (15 - 3√17)/2
D = 55 - 6√17
x1 = ( 5 - (55 - 6√17))/2
x2 = ( 5 + (55 - 6√17))/2

x^2 - 5x = (15 + 3√17)/2
D = 55 + 6√17
x1 = ( 5 - (55  + 6√17))/2
x2 = ( 5 + (55 + 6√17))/2