a^2+b^2+c^2=ab+ac+bc
则:2*a^2+2*b^2+2*c^2=2*ab+2*bc+2*ac
则:2*a^2+2*b^2+2*c^2-2*ab-2*bc-2*ac=0
则:(a^2+b^2-2*ab)+(c^2+a^2-2*ac)+(b^2+c^2-2*bc)=0
则:(a-b)^2+(a-c)^2+(b-c)^2=0
则:a=b,a=c,b=c,
则:a=b=c
则:等边三角形
a^2+b^2+c^2=ab+ac+bc
则:2*a^2+2*b^2+2*c^2=2*ab+2*bc+2*ac
则:2*a^2+2*b^2+2*c^2-2*ab-2*bc-2*ac=0
则:(a^2+b^2-2*ab)+(c^2+a^2-2*ac)+(b^2+c^2-2*bc)=0
则:(a-b)^2+(a-c)^2+(b-c)^2=0
则:a=b,a=c,b=c,
则:a=b=c
则:等边三角形