已知abc是三角形ABC的三边长,且满足a^4+b^4+c^4=a^2b^2+b^2c^2+c^2a^2
问题描述：
已知abc是三角形ABC的三边长,且满足a^4+b^4+c^4=a^2b^2+b^2c^2+c^2a^2
已知上条件,试问△ABC为何种三角形?
答
a^4+b^4+c^4=a^2b^2+b^2c^2+c^2a^22a^4+2b^4+2c^4=2a^2b^2+2b^2c^2+2c^2a^22a^4+2b^4+2c^4-2a^2b^2-2b^2c^2-2c^2a^2=0(a^2-b^2)^2+(b^2-c^2)^2+(a^2-c^2)^2=0(a^2-b^2)^2=0(b^2-c^2)^2=0(a^2-c^2)^2=0即a^2=b^2=c^2a...