Question

роз"яжіть систему рівнянь х²+у²=13
ху=6

Answer 1

$left { {{x^2+y^2=13} atop {xy=6}} right. ; left { {{x^2+y^2+2xy=13+12} atop {xy=6}} right. ; left { {{(x+y)^2=25} atop {xy=6}} right. ; left { {{x+y=pm 5} atop {xy=6}} right. \\a)quad left { {{x+y=5} atop {xy=6}} right. ; left { {{y=5-x} atop {x(5-x)=6}} right. ; left { {{y=5-x} atop {-x^2+5x-6=0}} right. ; left { {{y=5-x} atop {x^2-5x+6=0}} right. ; left { {{y_1=3; ,; y_2=2} atop {x_1=2; ,; x_2=3}} right.$

$b)quad left { {{x+y=-5} atop {xy=6}} right. ; left { {{y=-x-5} atop {x(-x-5)=6}} right. ; left { {{y=-x-5} atop {-x^2-5x-6=0}} right. ; left { {{y=-x-5} atop {x^2+5x+6=0}} right. ; left { {{y_1=-3; ,; y_2=-2} atop {x_1=-2; ,; x_2=-3}} right. \\Otvet;; ; (2,3),; (3,2),; (-2,-3),; (-3,-2) ; .$