(x^2 - 6x - 9)^2 - x(x^2 - 4x - 9) = 0 /:x^2 ≠ 0
(x - 6 - 9/x)^2 - (x - 4 - 9/x) = 0
Пусть x - 6 - 9/x = y, тогда
y^2 - (y + 2) = 0
y^2 - y - 2 = 0
D = 1 + 4*2 = 9
y1 =( 1 + 3)/2 = 4/2 = 2
y2 = (1 - 3 )/2 = - 2/2 = -1
1) x - 6 - 9/x = 2
x - 6 - 9/x - 2 = 0
x - 8 - 9/x = 0
x^2 - 8x - 9 = 0
D = 64 + 36 = 100
x1 = (8 + 10)/2 = 18/2 = 9
x2 = (8 - 10)/2 = - 2/2 = - 1
2) x - 6 - 9/x = - 1
x - 5 - 9/x = 0
x^2 - 5x - 9 = 0
D = 25 + 36 = 61
x3 = ( 5 + √61)/2 = 2,5 + √61/2
x4 = (5 - √61)/2 = 2,5 - √61/2
Ответ
- 1
9
2,5 - √61/2
2,5 + √61/2