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a2b2+a2+b2+10ab+16 =(a2b2+8ab+16)+(a2+2ab+b2) =(ab+4)2+(a+b)2 =0 所以(ab+4)2=0且(a+b)2=0 所以ab+4=0 且a+b=0 a=2,b=-2或者a=-2,b=2 所以a2+b2=4+4=8
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