a^4+b^4+c^4=a^2b^2+b^2c^2+c^2a^2
2(a^4+b^4+c^4)-2(a^2b^2+b^2c^2+c^2a^2)=0
(a^2-b^2)^2+(b^2-c^2)^2+(a^2-c^2)^2=0
a^2=b^2=c^2
a=b=c
等边三角形