Question

$left { {{(x-2)(y-2)=4} atop {x^{2}y + xy^{2}=72}} right.$

Answer 1

$left { {{(x-2)(y-2)=4} atop {x^2y+xy^2=72}} right. ; left { {{xy-2x-2y+4=4} atop {xy(x+y)=72}} right. ; left { {{xy=2(x+y)} atop {2(x+y)(x+y)=72}} right. ; left { {{xy=2(x+y)} atop {(x+y)^2=36}} right. \\left { {{xy=2(x+y)} atop {x+y=pm 6}} right. \\a); ; left { {{xy=2(x+y)} atop {x+y=6}} right. left { {{xy=12} atop {y=6-x}} right. ; left { {{x(6-x)=12} atop {y=6-x}} right. ; left { {{x^2-6x+12=0} atop {y=6-x}} right. \\x^2-6x+12=0; ,; D/4=3^2-12=-3<0; ,; xin varnothing$

$b); ; left { {{xy=2(x+y)} atop {x+y=-6}} right. left { {{xy=-12} atop {y=-x-6}} right. ; left { {{x(-x-6)=-12} atop {y=-x-6}} right. ; left { {{x^2+6x-12=0} atop {y=-x-6}} right. \\x^2+6x-12=0; ,; ; D/4=3^2+12=21; ,; ; x_{1/2}=-3pm sqrt{21}\\left { {{x=-3-sqrt{21}} atop {y=3+sqrt{21}-6}} right. ; left { {{x=-3-sqrt{21}} atop {y=-3+sqrt{21}}} right. \\left { {{x=-3+sqrt{21}} atop {y=3-sqrt{21}-6}} right. ; left { {{x=-3+sqrt{21}} atop {y=-3-sqrt{21}}} right. \\Otvet:; ; (-3-sqrt{21}; ,; -3+sqrt{21}); ,; (-3+sqrt{21}; ;; -3-sqrt{21}); .$