Б) х^3 -6х^2+9x>(x-3)^3

Решите задачу:

$x^3-6x^2+9x\ \textgreater \ (x-3)(x-3)(x-3) \\ x^3-6x^2+9x\ \textgreater \ (x^2-3x-3x+9)(x-3) \\ x^3-6x^2+9x\ \textgreater \ (x^2-6x+9)(x-3) \\ x^3-6x^2+9x\ \textgreater \ x^3-3x^2-6x^2+18x+9x-27 \\ x^3-6x^2+9x\ \textgreater \ x^3-9x^2+27x-27 \\ -6x^2+9x^2+9x-27x+27\ \textgreater \ 0 \\ 3x^2-18x+27\ \textgreater \ 0 \\ x^2-6x+9\ \textgreater \ 0 \\ D = 36-4*9=0 \\ x = 6/2=3 \\ (x-3)(x-3)\ \textgreater \ 0\\ (ifinity;3) U (3;infity)$