Question

(x-0.5)(x+2)^3+(0.5-x)(x-1)^3=9x-4.5 помогите пожалуйста

Answer 1

(x - 0.5)(x + 2)^3 + (0.5 - x)(x - 1)^3 = 9x - 4.5

(x - 0.5)(x + 2)^3 - (x - 0.5)(x - 1)^3 = 9(x - 0.5)

(x - 0.5)((x + 2)^3 - (x - 1)^3) = 9(x - 0.5)

x = 0.5 корень

(x + 2)^3 - (x - 1)^3 = 9

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

(x + 2 - x + 1)((x + 2)^2 + (x + 2)(x - 1) + (x - 1)^2) = 9

3(x^2 + 4x + 4 + x^2 + 2x - x - 2 + x^2 -2x + 1) = 9

x^2 + 4x + 4 + x^2 + 2x - x - 2 + x^2 -2x + 1 = 3

3x^2 + 3x = 0

x(x + 1) = 0

x = 0

x = -1

ответ x = {-1, 0, 0.5}