Решение
∛x = 2 - x
(∛x)³ = (2 - x)³
x = 2³ - 3*2²*x + 3*2*x² - x³
x³ - 6x² + 13x - 8 = 0
x1 = 1
x³ - 6x² + 13x - 8 I x - 1
-(x³ - x²) x² - 5x + 8
- 5x² + 13x
- (-5x² + 5x)
8x - 8
-(8x - 8)
0
(x - 1) * (x² - 5x + 8) = 0
x1 = 1
x² - 5x + 8 = 0
D = 25 - 4*1*8 = 25 - 32 = - 7 < 0 решений нет
Ответ: x = 1