若正整数x,y满足x^2+y^2=1=2x+2y,求x+y的值

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x²-2x+1+y²-2y+1=1
(x-1)²+(y-1)²=1
即两个整数的平方分是1
则0²+1²=1
不妨设(x-1)²=0,(y-1)²=1
所以x-1=0,y-1=1或x-1=0,y-1=-1
x=1,y=2
x=1,y=0
正整数则x=1,y=2
所以x+y=3

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