0\\ x^{2}-x<2\end{matrix}\right." alt="\left\{\begin{matrix}x^{2}-x>0\\ x^{2}-x<2\end{matrix}\right." align="absmiddle" class="latex-formula">
Решим каждое неравенство по отдельности.
Первое:
0\\x(x-1)>0\\\begin{bmatrix}\left\{\begin{matrix}x>0\\x-1>0\end{matrix}\right.\\\left\{\begin{matrix}x<0\\x-1<0\end{matrix}\right.\end{matrix}\\\\\begin{bmatrix}\left\{\begin{matrix}x>0\\x>1\end{matrix}\right.\\\left\{\begin{matrix}x<0\\x<1\end{matrix}\right.\end{matrix}\\\\\begin{bmatrix}x\in(1;+\infty)\\ x\in(-\infty;0)\end{matrix}\\x\in(-\infty;0)\cup(1;+\infty)" alt="x^{2}-x>0\\x(x-1)>0\\\begin{bmatrix}\left\{\begin{matrix}x>0\\x-1>0\end{matrix}\right.\\\left\{\begin{matrix}x<0\\x-1<0\end{matrix}\right.\end{matrix}\\\\\begin{bmatrix}\left\{\begin{matrix}x>0\\x>1\end{matrix}\right.\\\left\{\begin{matrix}x<0\\x<1\end{matrix}\right.\end{matrix}\\\\\begin{bmatrix}x\in(1;+\infty)\\ x\in(-\infty;0)\end{matrix}\\x\in(-\infty;0)\cup(1;+\infty)" align="absmiddle" class="latex-formula">
Второе:
0\end{matrix}\right.\\ \left\{\begin{matrix}x+1>0\\x-2<0\end{matrix}\right.\end{matrix}\\\\\begin{bmatrix}\left\{\begin{matrix}x<-1\\x>2\end{matrix}\right.\\ \left\{\begin{matrix}x>-1\\x<2\end{matrix}\right.\end{matrix}\\\\\begin{bmatrix}x\in\O\\x\in(-1;2)\end{matrix}\\x\in(-1;2)" alt="x^{2}-x<2\\x^{2}-x-2<0\\x^{2}+x-2x-2<0\\x(x+1)-2(x+1)<0\\(x+1)(x-2)<0\\\begin{bmatrix}\left\{\begin{matrix}x+1<0\\x-2>0\end{matrix}\right.\\ \left\{\begin{matrix}x+1>0\\x-2<0\end{matrix}\right.\end{matrix}\\\\\begin{bmatrix}\left\{\begin{matrix}x<-1\\x>2\end{matrix}\right.\\ \left\{\begin{matrix}x>-1\\x<2\end{matrix}\right.\end{matrix}\\\\\begin{bmatrix}x\in\O\\x\in(-1;2)\end{matrix}\\x\in(-1;2)" align="absmiddle" class="latex-formula">
Находим общее решение для системы неравенств:
0\\ x^{2}-x<2\end{matrix}\right.\\\\\left\{\begin{matrix}x\in(-\infty;0)\cup(1;+\infty)\\x\in(-1;2)\end{matrix}\right.\\x\in(-1;0)\cup(1;2)" alt="\left\{\begin{matrix}x^{2}-x>0\\ x^{2}-x<2\end{matrix}\right.\\\\\left\{\begin{matrix}x\in(-\infty;0)\cup(1;+\infty)\\x\in(-1;2)\end{matrix}\right.\\x\in(-1;0)\cup(1;2)" align="absmiddle" class="latex-formula">