1) 12x-3xy-2(x-3xy)=12x-3xy-2x+6xy=10x+3xy
2)10x-5=6(8x+3)-5x
10x-5=48x+18-5x
10x-5=43x+18
43x-10x=-5-18
33x=-23
x=-23/33
3) a)8xa+4xb=4x(2a+b)
4)2x^2-x=0
x(2x-1)=0
x=0
2x-1=0
2x=1
x=0,5
ответ :0;0,5
6) 3x(x+y+c)-3y(x-y-c)-3c(x+y-c)=3x^2+3xy+3xc-3xy+3y^2+3cy-3xc-3cy+3c^2=3x^2+3y^2+3c^2
Используем теорему Виета для квадратного уравнения.
![x_1+x_2=3\\ x_1x_2=-4](https://tex.z-dn.net/?f=x_1%2Bx_2%3D3%5C%5C%0Ax_1x_2%3D-4)
1)
![\frac{1}{x_1}+\frac{1}{x_2}=\frac{x_1+x_2}{x_1x_2}=\frac{3}{-4}=-\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx_1%7D%2B%5Cfrac%7B1%7D%7Bx_2%7D%3D%5Cfrac%7Bx_1%2Bx_2%7D%7Bx_1x_2%7D%3D%5Cfrac%7B3%7D%7B-4%7D%3D-%5Cfrac%7B3%7D%7B4%7D)
2)
![x_1^2+x_2^2=x_1^2+2x_1x_2+x_2^2-2x_1x_2=\\ (x_1+x_2)^2-2x_1x_2=3^2-2*(-4)=17](https://tex.z-dn.net/?f=x_1%5E2%2Bx_2%5E2%3Dx_1%5E2%2B2x_1x_2%2Bx_2%5E2-2x_1x_2%3D%5C%5C%0A%28x_1%2Bx_2%29%5E2-2x_1x_2%3D3%5E2-2%2A%28-4%29%3D17)