2a²+2b²+2c²-2ab-2bc-2ac=0=> (a²-2ab+b²)+(a²-2ac+c²)+(c²-2bc+b²)=0
(a-b)^2+(a-c)^2+(c-b)^2=0 三个完全平方（非负数）的和等于零的充分必要条件是它们分别等于零,所以(a-b)^2=0,(a-c)^2=0,(c-b)^2=0=> a-b=0,a-c=o,c-b=o
a=b=c,即 a,b,c相等.