Question

Решите систему уравнения 1)$left { {{ x^{2} - y^{2}=- 21}atop{x+y=-3}} right.$  2)$left { {{ x^{2} + y^{2}=74 } atop {x-y=2}} right.$ 

Answer 1

$x^2-y^2=-21\ x+y=3\ \ (x-y)(x+y)=-21\ x+y=-3\ \ x-y=7\ x+y=-3\ \ x=7+y\ 7+2y=-3\ 2y=-10\ y=-5\ x=2$

$x^2+y^2=74 \ x-y=2\ \ (x-y)^2+2xy=74\ x-y=2\ \ 2xy=70\ xy=35\ \ xy=35\ x-y=2\ \ x=2+y\ 2y+y^2=35\ y^2+2y-35=0\ D=12^2\ y_{1}=frac{-2+12}{2}=5\ y_{2}=frac{-2-12}{2}=-7\ x=7\ y=-5$