Question

Система уравнений
X+Y-8=0
X^2+Y^2=16+2XY

Answer 1

$begin{cases}x+y-8=0\x^2+y^2=16+2xyend{cases}Rightarrowbegin{cases}x=8-y\x^2-2xy+y^2=16end{cases}Rightarrow\Rightarrowbegin{cases}x=8-y\(x-y)^2=16end{cases}Rightarrowbegin{cases}x=8-y\(8-y-y)^2=16end{cases}\(8-y-y)^2=16\(8-2y)^2=16\begin{cases}8-2y=4\8-2y=-4end{cases}Rightarrowbegin{cases}y_1=2\y_2=6end{cases}\begin{cases}x_1=6\y_1=2end{cases}quadquadquadbegin{cases}x_2=2\y_2=6end{cases}\OTBET:;(6;;2),;(2;;6)$