Correct Answer - Option 4 : 1, 2 and 3

**Given: **

If a + b + c = 0

**Calculation **

We know that formula, a^{3 }+ b^{3 }+ c^{3 }– 3abc = (a + b + c) (a^{2} + b^{2} + c^{2} – ab – bc - ca)

Here put a + b + c = 0

Then, a^{3 }+ b^{3 }+ c^{3} - 3abc = 0

⇒ a3 + b3 + c3 = 3abc

Option (1) is correct

We know that a^{2} + b^{2} + c^{2} = (a + b + c)^{2} – 2(ab + bc + ca)

Put a + b + c = 0

Then, a^{2} + b^{2} + c^{2} = – 2(ab + bc + ca)

Option (2) is correct.

From above, a3 + b3 + c3 = 3abc

From the question, c = -(a + b)

⇒ a3 + b3 + c3 = -3ab(a + b)

Option (3) is correct

Hence, 1, 2 and 3 are correct.