Question

设a、b、c为三角形ABC的三边长,且满足a³+b³+c³=3abc,求证三角形ABC是正

Answer 1

a3+b3+c3-3abc=0

=>(a+b+c)(a2+b2+c2-ab-bc-ca)=0

since a+b+c!=0

then a2+b2+c2-ab-bc-ca=0

=>(a-b)^2+(b-c)^2+(c-a)^2=0

=>a=b=c

=>结论