Question

Постройте график уравнения ( y+2x)•(y-x-1)=0

Answer 1

$(y+2x)\cdot(y-x-1)=0, \\ y^2-xy-y+2xy-2x^2-2x = 0, \\ y^2+xy-y-2x^2-2x=0, \\ y^2+y(x-1)-2x^2-2x=0, \\ D=(x-1)^2-4(-2x^2-2x)=x^2-2x+1+8x^2+8x=\\=9x^2+6x+1=(3x+1)^2, \\ y=\frac{1}{2}(-(x-1)\pm\sqrt{(3x+1)^2})=\frac{1}{2}(1-x\pm|3x+1|), \\ y= \left [ {{x+1,} \atop {-2x.}} \right.$