若实数x,y满足（x+2y-2)(3x+2y+2)+2(x2+4)=0,求x+y的值.如题,请详细.

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若实数x,y满足（x+2y-2)(3x+2y+2)+2(x2+4)=0,求x+y的值.如题,请详细.

若实数x,y满足（x+2y-2)(3x+2y+2)+2(x2+4)=0,求x+y的值.如题,请详细.
若实数x,y满足（x+2y-2)(3x+2y+2)+2(x2+4)=0,求x+y的值.
如题,请详细.

若实数x,y满足（x+2y-2)(3x+2y+2)+2(x2+4)=0,求x+y的值.如题,请详细.
∵(x+2y-2)(3x+2y+2)+2(x^2+4)
=（2x+2y-x-2)(2x+2y+x+2)+2(x^2+4)
= [(2x+2y)-(x+2)][(2x+2y)+(x+2)]+2(x^2+4)
= (2x+2y)^2-(x+2)^2+2x^2+8
= (2x+2y)^2-x^2-4x-4+2x^2+8
= (2x+2y)^2+(x^2-4x+4)
= (2x+2y)^2+(x-2)^2
= 0
又∵(2x+2y)^2≥0,(x-2)^2≥0,
∴ (2x+2y)^2=(x-2)^2=0
∴2(x+y)=2x+2y=0
∴x+y=0

拆开，5x2+8xy-4x+4y2+4=0
令y=t-x带入
得4t2+x2-4x+4=0
得t=0呢，感觉不对呢

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