а паподробнее напиши а лучше фотку выложы а то я запутался в этих дробях
4) (√10 - 2 ) ( √10 + 2 )= (√10)^2-2^2=10-4=6, поскольку нет корня ето и есть рациональное число.
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![\left\{\begin{matrix}x^{2}-x>0\\ x^{2}-x<2\end{matrix}\right.](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Bmatrix%7Dx%5E%7B2%7D-x%3E0%5C%5C%20x%5E%7B2%7D-x%3C2%5Cend%7Bmatrix%7D%5Cright.)
Решим каждое неравенство по отдельности.
Первое:
![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)](https://tex.z-dn.net/?f=x%5E%7B2%7D-x%3E0%5C%5Cx%28x-1%29%3E0%5C%5C%5Cbegin%7Bbmatrix%7D%5Cleft%5C%7B%5Cbegin%7Bmatrix%7Dx%3E0%5C%5Cx-1%3E0%5Cend%7Bmatrix%7D%5Cright.%5C%5C%5Cleft%5C%7B%5Cbegin%7Bmatrix%7Dx%3C0%5C%5Cx-1%3C0%5Cend%7Bmatrix%7D%5Cright.%5Cend%7Bmatrix%7D%5C%5C%5C%5C%5Cbegin%7Bbmatrix%7D%5Cleft%5C%7B%5Cbegin%7Bmatrix%7Dx%3E0%5C%5Cx%3E1%5Cend%7Bmatrix%7D%5Cright.%5C%5C%5Cleft%5C%7B%5Cbegin%7Bmatrix%7Dx%3C0%5C%5Cx%3C1%5Cend%7Bmatrix%7D%5Cright.%5Cend%7Bmatrix%7D%5C%5C%5C%5C%5Cbegin%7Bbmatrix%7Dx%5Cin%281%3B%2B%5Cinfty%29%5C%5C%20x%5Cin%28-%5Cinfty%3B0%29%5Cend%7Bmatrix%7D%5C%5Cx%5Cin%28-%5Cinfty%3B0%29%5Ccup%281%3B%2B%5Cinfty%29)
Второе:
![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)](https://tex.z-dn.net/?f=x%5E%7B2%7D-x%3C2%5C%5Cx%5E%7B2%7D-x-2%3C0%5C%5Cx%5E%7B2%7D%2Bx-2x-2%3C0%5C%5Cx%28x%2B1%29-2%28x%2B1%29%3C0%5C%5C%28x%2B1%29%28x-2%29%3C0%5C%5C%5Cbegin%7Bbmatrix%7D%5Cleft%5C%7B%5Cbegin%7Bmatrix%7Dx%2B1%3C0%5C%5Cx-2%3E0%5Cend%7Bmatrix%7D%5Cright.%5C%5C%20%5Cleft%5C%7B%5Cbegin%7Bmatrix%7Dx%2B1%3E0%5C%5Cx-2%3C0%5Cend%7Bmatrix%7D%5Cright.%5Cend%7Bmatrix%7D%5C%5C%5C%5C%5Cbegin%7Bbmatrix%7D%5Cleft%5C%7B%5Cbegin%7Bmatrix%7Dx%3C-1%5C%5Cx%3E2%5Cend%7Bmatrix%7D%5Cright.%5C%5C%20%5Cleft%5C%7B%5Cbegin%7Bmatrix%7Dx%3E-1%5C%5Cx%3C2%5Cend%7Bmatrix%7D%5Cright.%5Cend%7Bmatrix%7D%5C%5C%5C%5C%5Cbegin%7Bbmatrix%7Dx%5Cin%5CO%5C%5Cx%5Cin%28-1%3B2%29%5Cend%7Bmatrix%7D%5C%5Cx%5Cin%28-1%3B2%29)
Находим общее решение для системы неравенств:
![\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)](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Bmatrix%7Dx%5E%7B2%7D-x%3E0%5C%5C%20x%5E%7B2%7D-x%3C2%5Cend%7Bmatrix%7D%5Cright.%5C%5C%5C%5C%5Cleft%5C%7B%5Cbegin%7Bmatrix%7Dx%5Cin%28-%5Cinfty%3B0%29%5Ccup%281%3B%2B%5Cinfty%29%5C%5Cx%5Cin%28-1%3B2%29%5Cend%7Bmatrix%7D%5Cright.%5C%5Cx%5Cin%28-1%3B0%29%5Ccup%281%3B2%29)