a2 + b2 + c2 -ab- bc - ca = 0, iff

Here given formula is 

$a2 + b2 + c2 -\mathrm{ab}- \mathrm{bc} - \mathrm{ca} = 0$

and it is possible if and only if a = b = c.

From the trial and error method, 

1) Let a = b = c = 1

Now substitute these values of a, b, c in the above formula.

We get 1 + 1 + 1 - 1 - 1 - 1 = 3 - 3 = 0

2) Now, let a = b = c = 4

Now substitute these values of a, b, c in the above formula.

We get 16 + 16 + 16 - 16 - 16 - 16 = 48 - 48 = 0.

Hence, it is possible that 

$a2 + b2 + c2 -\mathrm{ab}- \mathrm{bc} - \mathrm{ca} = \mathrm{0\; iff \; a\; =\; b\; =\; c.}$