(1)x^2-4y^2+x+3y-1=02x-y-1=0(2)x-y+5=0x^2+y^2=625(3)2x-y^2=0x^2+y^2=8(4)x^2+y^2=5xy=2
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(1)x^2-4y^2+x+3y-1=0
2x-y-1=0
(2)x-y+5=0
x^2+y^2=625
(3)2x-y^2=0
x^2+y^2=8
(4)x^2+y^2=5
xy=2
1.
由②得 y=2x-1
将y=2x-1代入①
x^2-4(2x-1)^2+x+3(2x-1)-1=0
经过整理后得:
15x^2-23x+8=0
(15x-8)(x-1)=0
x=8/15,y=16/15-1=1/15
x=1,y=2-1=1
所以x=8/15,y=1/15或 x=1,y=1
2.
由①得 y=x+5
代入②得 x^2+(x+5)^2=625
x^2+5x-300=0
(x+20)(x-15)=0
x=-20,y=-15
x=15,y=20
3.
由①得 y^2=2x
代入② x^2+2x=8
x^2+2x-8=0
(x+4)(x-2)=0
x=-4(舍)
x=2,y^2=2*2=4
y=2 or -2
所以,x=2,y=2或者 x=2,y=-2
4.
由②得 x=2/y
代入①得 4/y^2+y^2=5
设y^2=a
4/a+a=5
4+a^2=5a
a^2-5a+4=0
(a-1)(a-4)=0
一.a=1
y^2=1
y=1,x=2
y=-1,x=-2
二.a=4
y^2=4
y=2,x=1
y=-2,x=-1
综上所述:
x=2,y=1
x=-2,y=-1
x=1,y=2
x=-1,y=-2
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