a2 + b2 + c2 -ab- bc - ca = 0, iff abc = -1 a = b = c abc = 1 abc = 0 Here given

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Correct Answer

a = b = c

Explanation

Here given formula is

$a^{2} + b^{2} + c^{2} - ab - bc - ca = 0$

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

$a^{2} + b^{2} + c^{2} - ab - bc - ca = 0 iff a = b = c.$

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