a²+c²=2ab+2bc-2b²a²+2b²+c²-2ab-2bc=0(a²-2ab+b²)+(b²-2bc+c²)=0(a-b)²+(b-c)²=0因此,a-b=0,且 b-c=0则 a=b=c三角形ABC是等边三角形