x = 1.6(1)
10x = 16.(1)
100x = 161.(1)
100x - 10x = 161.(1) - 16.(1)
90x = 145
x = 145/90 = 29/18
По формуле сокращенного умножения разность квадратов
Все решается методом интервалов:
6)
![|7x-12|-|7x-11|=1;\\ \begin{cases}7x-12=0,\\ 7x-11=0;\end{cases}\,\begin{cases}x=\frac{12}{7},\\ x=\frac{11}{7};\end{cases}\,x\in(-\infty;\frac{11}{7})\cup[\frac{11}{7}; \frac{12}{7})\cup[\frac{12}{7};+\infty).\\ 1) x\in(-\infty;\frac{11}{7}), \,-7x+12+7x-11=1;\,1=1; x\in(-\infty;\frac{11}{7});\\ 2) x\in[\frac{11}{7}; \frac{12}{7}), \,-7x+12-7x+11=1;\\ -14x=-22;\,x=\frac{22}{14}=\frac{11}{7}.\\ 3) x\in[\frac{12}{7};+\infty),\, 7x-12-7x+11=1;\,-1=1; \{\emptyset\}.](https://tex.z-dn.net/?f=%7C7x-12%7C-%7C7x-11%7C%3D1%3B%5C%5C%0A%5Cbegin%7Bcases%7D7x-12%3D0%2C%5C%5C%0A7x-11%3D0%3B%5Cend%7Bcases%7D%5C%2C%5Cbegin%7Bcases%7Dx%3D%5Cfrac%7B12%7D%7B7%7D%2C%5C%5C%0Ax%3D%5Cfrac%7B11%7D%7B7%7D%3B%5Cend%7Bcases%7D%5C%2Cx%5Cin%28-%5Cinfty%3B%5Cfrac%7B11%7D%7B7%7D%29%5Ccup%5B%5Cfrac%7B11%7D%7B7%7D%3B+%5Cfrac%7B12%7D%7B7%7D%29%5Ccup%5B%5Cfrac%7B12%7D%7B7%7D%3B%2B%5Cinfty%29.%5C%5C%0A1%29+x%5Cin%28-%5Cinfty%3B%5Cfrac%7B11%7D%7B7%7D%29%2C+%5C%2C-7x%2B12%2B7x-11%3D1%3B%5C%2C1%3D1%3B+x%5Cin%28-%5Cinfty%3B%5Cfrac%7B11%7D%7B7%7D%29%3B%5C%5C%0A2%29+x%5Cin%5B%5Cfrac%7B11%7D%7B7%7D%3B+%5Cfrac%7B12%7D%7B7%7D%29%2C+%5C%2C-7x%2B12-7x%2B11%3D1%3B%5C%5C%0A-14x%3D-22%3B%5C%2Cx%3D%5Cfrac%7B22%7D%7B14%7D%3D%5Cfrac%7B11%7D%7B7%7D.%5C%5C%0A3%29+x%5Cin%5B%5Cfrac%7B12%7D%7B7%7D%3B%2B%5Cinfty%29%2C%5C%2C+7x-12-7x%2B11%3D1%3B%5C%2C-1%3D1%3B+%5C%7B%5Cemptyset%5C%7D.)
Ответ:
![x\in(-\infty;\frac{11}{7}].](https://tex.z-dn.net/?f=x%5Cin%28-%5Cinfty%3B%5Cfrac%7B11%7D%7B7%7D%5D.)
![|x-3|+|x+2|-|x-4|=3;\\ x\in(-\infty;-2)\cup[-2; 3)\cup[3; 4)\cup[4;+\infty).\\ 1) x\in(-\infty;2);\\ -x+3-x-2+x-4=3;\\ -x=6;\,x=-6.\\ 2) x\in[-2; 3);\\ -x+3+x+2+x-4=3;\\ x=2;\\ 3) x\in[3;+4);\\ x-3+x+2+x-4=3;\\ 3x=8;\,x=\frac{8}{3}\notin [3;+4);\\ 4) x\in[4;\infty);\\ x-3+x+2-x+4=3;\\ x=0\notin [4;\infty).](https://tex.z-dn.net/?f=%7Cx-3%7C%2B%7Cx%2B2%7C-%7Cx-4%7C%3D3%3B%5C%5C%0Ax%5Cin%28-%5Cinfty%3B-2%29%5Ccup%5B-2%3B+3%29%5Ccup%5B3%3B+4%29%5Ccup%5B4%3B%2B%5Cinfty%29.%5C%5C%0A1%29+x%5Cin%28-%5Cinfty%3B2%29%3B%5C%5C%0A-x%2B3-x-2%2Bx-4%3D3%3B%5C%5C%0A-x%3D6%3B%5C%2Cx%3D-6.%5C%5C%0A2%29+x%5Cin%5B-2%3B+3%29%3B%5C%5C%0A-x%2B3%2Bx%2B2%2Bx-4%3D3%3B%5C%5C%0Ax%3D2%3B%5C%5C%0A3%29+x%5Cin%5B3%3B%2B4%29%3B%5C%5C%0Ax-3%2Bx%2B2%2Bx-4%3D3%3B%5C%5C%0A3x%3D8%3B%5C%2Cx%3D%5Cfrac%7B8%7D%7B3%7D%5Cnotin+%5B3%3B%2B4%29%3B%5C%5C%0A4%29+x%5Cin%5B4%3B%5Cinfty%29%3B%5C%5C%0Ax-3%2Bx%2B2-x%2B4%3D3%3B%5C%5C%0Ax%3D0%5Cnotin+%5B4%3B%5Cinfty%29.)
Ответ:
![x_1=-6,\,x_2=2.](https://tex.z-dn.net/?f=x_1%3D-6%2C%5C%2Cx_2%3D2.)
(а+1/2а - 2 + 6/2а² - 2 + а+3/2а+2) * 4а² - 4/3 =
(а+1/2(а-1) + 6/2(а²-1) + а+3/2(а+1)) * 4а² - 4/3 =
((а+1)²/2(а-1)(a+1) + 6/2(а-1)(a+1) + (а+3)(a-1)/2(а+1)(a-1)) * 4а² - 4/3 =
(а²+2a+1+6+ а²+3a-a-3)/2(а+1)(a-1)) * 4а² - 4/3 =
(2а²+4a+4)/2(а+1)(a-1)) * 4а² - 4/3 =
2(а²+2a+2)/2(а+1)(a-1)) * 4а² - 4/3 =
4a²(а²+2a+2)/(а+1)(a-1) - 4/3 =
12a²(а²+2a+2)-4 / 3(а+1)(a-1) =
4(3a²(а²+2a+2)-1) / 3(a²-1)
как-то так