Question

х^3-х^2>2х неравенствооо

Answer 1

$x^3-x^2 textgreater 2x\\ x^3-x^2-2x textgreater 0\\ x(x^2-x-2) textgreater 0\\ x=0\\\ x^2-x-2=0\\ x^2-x=2\\ x^2- frac{x}{2}+ frac{1}{4}=2+ frac{1}{4}\\ (x- frac{1}{2})^2= frac{9}{4}\\ sqrt{(x- frac{1}{2})^2} = sqrt{ frac{9}{4}}\\ |x- frac{1}{2}|=pm frac{3}{2}\\ x- frac{1}{2}=- frac{3}{2}\\ x=- frac{3}{2}+ frac{1}{2}\\ x_1=-1\\\ x- frac{1}{2}= frac{3}{2}\\ x= frac{3}{2}+ frac{1}{2}\\ x_2=2\\ xin(-1;0)bigcup(2;+infty)$