a^4+b^4+c^4=a^2b^2+b^2c^2+c ^2a^2,
2a^4+2b^4+2c^4=2a^2b^2+2b^2c^2+2c ^2a^2,
(a4-2a^2b^2+b^4)+(b^4-2b^2c^2+c^4)+(c^4-2c^2a^2+a^4)=0,
(a^2-b^2)^2+(b^2-c^2)^2+(c^2-a^2)^2=0,
当且仅当a^2-b^2=0,b^2-c^2=0,c^2-a^2=0时等式方成立,
故a=b=c,
三角形是等边三角形.