a^2+b^2+c^2-ab-bc-ac=0
两边同乘以2得:
2a^2+2b^2+2c^2-2ab-2bc-2ac=0
(a-b)²+(a-c)²+(b-c)²=0
则必有:
a-b=a-c=b-c=0
解得:
a=b=c