Question

б) х^3 -6х^2+9x>(x-3)^3

Answer 1

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