Question

if a square + b square + c square minus ab minus bc minus ca equals to zero, prove that A equals to B equal to C

Answer 1

A^2 + b^2 + c^2  - ab - bc - ca = 0
a.a + b.b + c.c = a.b + b.c + c.a

equating  term by term:- 
a = b
b = c 
c = a

Therefore a = b = c