(1)3x^2-y^2=8 x^2+xy+y^2=4 (2)x^2+y^2=4 xy-y^2+4=0
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(1)3x^2-y^2=8 x^2+xy+y^2=4 (2)x^2+y^2=4 xy-y^2+4=0
(3)4x^2+12xy+9y^2=1 4x^2-y^2=0 (4)x^2+2xy+y-64=0 6x^2+xy-2y^2=0
都是同类型,解答一两题或几题来参考,第一次写不知道怎么写
(3)4x^2+12xy+9y^2=1 4x^2-y^2=0 (4)x^2+2xy+y-64=0 6x^2+xy-2y^2=0
都是同类型,解答一两题或几题来参考,第一次写不知道怎么写
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
=>
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
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