(a+b+c)^2=3ab+3bc+3ca
a^2+b^2+c^2+2ab+2bc+2ac-3ab-3bc-3ca=0
a^2+b^2+c^2-ab-bc-ac=0
2a^2+2b^2+2c^2-2ab-2bc-2ac=0
a^2-2ab+b^2+(a^2-2ac+c^2)+(b^2-2bc+c^2)=0
(a-b)^2+(a-c)^2+(b-c)^2=0
所以,a-b=0,a-c=0,b-c=0
a=b,a=c,b=c
a=b=c,
所以,三角形是等边三角形.
(a+b+c)^2=3ab+3bc+3ca
a^2+b^2+c^2+2ab+2bc+2ac-3ab-3bc-3ca=0
a^2+b^2+c^2-ab-bc-ac=0
2a^2+2b^2+2c^2-2ab-2bc-2ac=0
a^2-2ab+b^2+(a^2-2ac+c^2)+(b^2-2bc+c^2)=0
(a-b)^2+(a-c)^2+(b-c)^2=0
所以,a-b=0,a-c=0,b-c=0
a=b,a=c,b=c
a=b=c,
所以,三角形是等边三角形.