Среднее арифметическое корней уравнения равно

(х-0,5) (х+2) ³ + (0,5-х) (х-1) ³=9 х-4,5

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

x1=1/2

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

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

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

(2x+1) (x^2+x+7) = 9

2x^3+x^2+2x^2+x+14x+7=9

2x^3+3x^2+15x-2=0

x^3+3/2x^2+15/2x-1=0

x2+x3+x4=-3/2

x1+x2+x3+x4=1/2-3/2=-1

(x1+x2+x3+x4) / 4=-1/4

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

x1=1/2

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

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

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

(2x+1) (x^2+x+7) = 9

2x^3+x^2+2x^2+x+14x+7=9

2x^3+3x^2+15x-2=0

x^3+3/2x^2+15/2x-1=0

x2+x3+x4=-3/2

x1+x2+x3+x4=1/2-3/2=-1

(x1+x2+x3+x4) / 4=-1/4