a²+b²+2a-8b+17=0
(a²+2a+1)+(b²-8b+16)-1-16+17=0
(a+1)²+(b-4)²=0
两个非负数之和为0,则两个非负数都为0
即：(a+1)²=0,(b-4)²=0
解得：a=-1,b=4
∴a+b=-1+4=3
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