等边三角形a^2+b^2+c^2=ab+ac+bc2a^2+2b^2+2c^2=2ab+2ac+2bc2a^2+2b^2+2c^2-2ab-2ac-2bc=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∴a-b=0 a-c=0 b-c=0∴a=b a=c b=c即a=b=c得等边三角形
