Question

Ситема: ху+х-у=7 ; х^2у-у^2х=6

Answer 1

$left { {{xy+x-y=7} atop {x^2y-xy^2=6}} right. ; left { {{xy+x-y=7} atop {xy(x-y)=6}} right. ; ; ; u=x-y; ,; ; v=xy\\ left { {{u+v=7} atop {uv=6}} right. ; left { {{u=7-v} atop {(7-v)v=6}} right. ; left { {{u=7-v} atop {v^2-7v+6=0}} right. ; left { {{u_1=6; ,; u_2=1} atop {v_1=1; ,; v_2=6}} right. \\a); ; left { {{x-y=6} atop {xy=1}} right. ; left { {{y=x-6} atop {x(x-6)=1}} right. ; left { {{y=x-6} atop {x^2-6x-1=0}} right. \\x^2-6x-1=0; ,; ; frac{D}{4} =3^2+1=10; ,; ; x_{1,2}=3pm sqrt{10}$

$y_1=x_1-6=3-sqrt{10}-6=-3- sqrt{10} \\y_2=x_2-6=3+sqrt{10}-6=-3+sqrt{10} \\b); ; left { {{x-y=1} atop {xy=6}} right. ; left { {{y=x-1} atop {x(x-1)=6}} right. ; left { {{y=x-1} atop {x^2-x+6=0}} right. \\x^2-x+6=0; ,; ; D=1-24=-23 textless 0; ; Rightarrow ; ; xin varnothing \\Otvet:; ; (3-sqrt{10}, ;, -3-sqrt{10}); ,; ; (3+sqrt{10}, ;, -3+sqrt{10}); .$