Question

Решите пожалуйста систему уравнений

Answer 1

$left { {{x^2+y^2+4x-6y=13} atop {xy-3x+2y=11}} right.; left { {{(x^2+y^2-2xy)+2xy=13-4x+6y} atop {xy=11+3x-2y}} right. \\left { {{(x-y)^2=13-4x+6y-2xy} atop {xy=11+3x-2y}} right.; left { {{(x-y)^2=13-4x+6y-2(11+3x-2y)} atop {xy=11+3x-2y}} right.\\left { {{(x-y)^2=-9-10x+10y} atop {xy=11+3x-2y}} right.; left { {{(x-y)^2=-9-10(x-y)} atop {xy=11+3x-2y}} right. \\(x-y)^2+10(x-y)+9=0\\t=x-y; ; Rightarrow ; ; t^2+10t+9=0; ,; ; t_1=-1; ,; t_2=-9; (teorema; Vieta)$

$a); ; x-y=-1; to ; x=y-1\\(y-1)cdot y=11+3(y-1)-2y\\y^2-y=11+3y-3-2y\\y^2-2y-8=0; ,; ; y_1=-2; ,; y_2=4; ; (teorema; Vieta)\\x_1=-2-1=-3; ,; ; x_2=4-1=3\\(-3,-2); ,; ; (3,4)\\b); ; x-y=-9; ; to ; ; x=y-9\\(y-9)cdot y=11+3(y-9)-2y\\y^2-9y=11+3y-27-2y\\y^2-10y+16=0; ,; ; y_1=2; ,; ; y_2=8; ; (teorema; Vieta)\\x_1=2-9=-7; ,; ; x_2=8-9=-1\\(-7,2); ,; ; (-1,8)\\Otvet:; ; (-3,-2); ,; (3,4); ,; (-7,2); ,; (-1,8); .$