解方程组:x^2-2xy-y^2+2x+y+2=0,2x^2-4xy-2y^2+3x+3y+4=0
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解方程组:x^2-2xy-y^2+2x+y+2=0,2x^2-4xy-2y^2+3x+3y+4=0
x^2-2xy-y^2+2x+y+2=0,(1)
2x^2-4xy-2y^2+3x+3y+4=0 ,(2)
(1)式*2得
2x^2-4xy-2y^2+4x+2y+4=0,(3)
(2)式-(3)式得
-x+y=0
x=y
代入(1)
y^2-2y^2-y^2+2y+y+2=0
2y^2-3y-2=0
(y-2)(2y+1)=0
y1=2,y2=-1/2
x1=2,x2=-1/2
解是;
x1=y1=-1/2,x2=y2=2
两组解
2x^2-4xy-2y^2+3x+3y+4=0 ,(2)
(1)式*2得
2x^2-4xy-2y^2+4x+2y+4=0,(3)
(2)式-(3)式得
-x+y=0
x=y
代入(1)
y^2-2y^2-y^2+2y+y+2=0
2y^2-3y-2=0
(y-2)(2y+1)=0
y1=2,y2=-1/2
x1=2,x2=-1/2
解是;
x1=y1=-1/2,x2=y2=2
两组解
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