Question

If a 2 + b 2 + c 2 -ab-bc-ca=0 then prove: a=b=c

Answer 1

a^2+ b^2 + c^2 - ab + bc + ac =0 

so ( a-b)^2=0  or a= b 
(b-c)^2 =0       or b = c 
(c-a )^2 =0      or c = a 

so a = b = c proved