Question

（1）3x^2-y^2=8 x^2+xy+y^2=4 （2)x^2+y^2=4 xy-y^2+4=0

Answer 1

x^2+xy+y^2=4

=>

2x^2+2xy+2y^2=8

联立3x^2-y^2=8

相减得

=>

x^2-2xy-3y^2=0

=>

(x-3y)(x+y)=0

=>

x=3y或x=-y

讨论：

1)x=3y

=>

3(3y)^2-y^2=8

=>

26y^2=8

=>

y=正负（根号（4/13））

x=正负3*（根号（4/13））

2)x=-y

=>

(-y)^2+(-y)*y+y^2=4

=>

y^2=4

=>

y=正负2

=>

x=负正2