Question

Решите уравнение
(x+2)^3=x^3+8
(3x-1)^3=27x^3-1

Answer 1

1)(x+2)³ = x³+8

(x+2)³ - (x+2)(x²-2x+4) = 0

(x+2)((x+2)²-(x²-2x+4)) = 0

(x+2)(x²+4x+4-x²+2x-4) = 0

(x+2)•6x = 0

[x+2 = 0

[6x = 0

x = -2

x = 0

2)(3x-1)³ = 27x³-1

(3x-1)³ - (3x-1)(9x²+3x+1) = 0

(3x-1)((3x-1)²-(9x²+3x+1)) = 0

(3x-1)(9x²-6x+1-9x²-3x-1) = 0

-9x(3x-1) = 0

[-9x = 0

[3x -1 = 0

x1 = 0

3x2 = 1

x2 = 1/3