Question

Помогите решить систему xy-x=2, xy^3-xy^2=8

Answer 1

$left { {{xy-x=2} atop {xy^3-xy^2=8}} right. = textgreater left { {{xy-x=2} atop {x(y^3-y^2)=8}} right. = textgreater left { {{frac{8y}{y^3-y^2}-frac{8}{y^3-y^2}=2 (*)} atop {x=frac{8}{y^3-y^2}}} right. \ \ (*) frac{8y}{y^3-y^2}-frac{8}{y^3-y^2}=2 | * (y^3-y^2) y neq 0; 1.\ \ 8y-8=2y^3-2y^2 | : 2 \ \ y^3-y^2-4y+4 = 0 \ \ y^2*(y-1)-4*(y-1)=0 \ \ (y-1)*(y^2-4) = 0 \ \ (y-1)*(y-2)(y+2) = 0 = textgreater y = б2.$
$y=2 : x=frac{8}{2^3-2^2} = frac{8}{4}=2 \ \ y=-2 : x=frac{8}{(-2)^3-(-2)^2}=frac{8}{-12} = -frac{2}{3} \ \ \ OTBET: (-frac{2}{3}; -2), (2; 2).$[