Correct Answer - Option 4 : 1, 2 and 3
Given:
If a + b + c = 0
Calculation
We know that formula, a3 + b3 + c3 – 3abc = (a + b + c) (a2 + b2 + c2 – ab – bc - ca)
Here put a + b + c = 0
Then, a3 + b3 + c3 - 3abc = 0
⇒ a3 + b3 + c3 = 3abc
Option (1) is correct
We know that a2 + b2 + c2 = (a + b + c)2 – 2(ab + bc + ca)
Put a + b + c = 0
Then, a2 + b2 + c2 = – 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.