Question

1)x^2+y^2=74
x-y=2
2)x^2+4y^2=34
x+y=7
3)x^2-2xy-y^2=1
x+y=2

Answer 1

1) x^2+y^2=74
X=2+y
(2+y)^2+y^2=74
4+4y+y^2+y^2=74
2y^2+4y-70=0Y^2+2y-35=0D=4+140=144
y1=5
y2=-7 => x1=2+5=7; x2=2+(-7)=-5

2)x^2+4y^2=34
x+y=7
x=7-y 
(7-y)^2+4y^2=34
49-14y+y^2+4y^2-34=0
5y^2-14y+15=0
D=196-300=-104
Корней нет
3) x^2-2xy-y^2=1
x+y=2
y=2-xx^2-2x*(2-x)-(2-x)^2=1
x^2-4x+2x^2-4-4x+x^2-1=0
4x^2-8x-5=0
D=64+80=144
x1=2,5; x2=-0,5;
y=2-x => y1=2-2,5=-0,5; y2=2-(-0,5)=2+0,5=2,5