x^2+y^2-8x+10y+41=0求(x+y)^2013

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x^2+y^2-8x+10y+41=0求(x+y)^2013
x^2+y^2-8x+10y+41=0求(x+y)^2013

x^2+y^2-8x+10y+41=0求(x+y)^2013
x^2+y^2-8x+10y+41=0
(x-4)^2+(y+5)^2=0
x=4,y= - 5
x+y=-1
(x+y)^2013=-1

整理得(x^2-8x+16)+(y^2+10y+25)=0 因为16+25=41
故(x-4)^2+(y+5)^2=0
即x=4 y=-5
x+y=-1
(x+y)^2013=-1

化简方程式可得：（x-4）^2+（y+5）^2=0，所以x=4，y=-5，所以x+y=-1，所以（x+y）^2013=负一

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