Question

if a²+b²+c²-ab-bc-ca=0 prove that a=b=c

Answer 1

a²+b²+c²-ab-bc-ca = 0
a²+b²+c² = ab+bc+ca
this is possible only and only if
a² = a b it implies....a cut with a and hence a=b
b² = bc, it implies...b cut with b and hence b=c
c² = ac. it implies..c cut with c and hence c = a
so all abive results implies.....
a=b=c
........