Question

Решить уравнение 100 баллов

Answer 1

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Answer 2

∛(3x + 6) - ∛(x + 1) = 1

∛(3x + 6) = a

∛(x + 1) = b

a - b = 1

a³ - 3b³ = 3

a = b + 1

(b + 1)³ - 3b³ = 3

b³ + 3b² + 3b + 1 - 3b³ - 3 = 0

-2b³ - 2 + 3b² + 3b = 0

-2(b³ + 1) + 3b(b + 1) = 0

-2(b + 1)(b² - b + 1) + 3b(b + 1) = 0

(b + 1)(-2b² + 2b - 2 + 3b) = 0

(b + 1)(2b²  -5b + 2) = 0

b = -1

D = 25 - 4*4 = 9

b23 = (5 +- 3)/4 = 2   1/2

1. b = -1

∛(x + 1) = -1

x + 1 = -1

x = -2

проверяем

∛(-6 + 6) - ∛(-2 + 1) = 0 - (-1) = 1 да

2. b = 2

∛(x + 1) = 2

x + 1 = 8

x = 7

проверяем

∛(21 + 6) - ∛(7 + 1) = 3 - 2 = 1 да

3. b = 1/2

∛(x + 1) = 1/2

x + 1 = 1/8

x = -7/8

проверяем

∛(-21/8 + 6) - ∛(-7/8 + 1) =∛(-21/8 + 48/8) - ∛ 1/8 = 3/2 - 1/2 = 1 да

Ответ x = {-2,-7/8,7}