Question

Срочно! Решите уравнение $\sqrt[3]{x+5} -\sqrt[3]{x-4} =3$

Answer 1

∛(x + 5) - ∛(x - 4) = 3

∛(x + 5) = a

∛(x - 4) = b

Система

a - b = 3

a³ - b³ = 9

a³ - b³ = (a - b)(a² + ab + b²) = (a - b)((a - b)² + 3ab) = 3(9 + 3ab) = 9

3 + ab = 1

a = 3 + b

3 + b(3 + b) = 1

b² + 3b + 2 = 0

D = 9 - 8 = 1

b12= (-3 +- 1)/2 = -2   -1

1. b = -2

∛(x - 4) = -2

x = -4

2. b = -1

∛(x - 4) = -1

x = 3

ответ x = {-4,3}