# If a + b + c = 0, then which of the following are correct? 1. a3 + b3 + c3 = 3abc 2. a2 + b2 + c2 = -2(ab + bc + ca) 3. a3 + b3 + c3 = -3ab(a + b) Sel

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If a + b + c = 0, then which of the following are correct?

1. a3 + b3 + c3 = 3abc

2. a2 + b2 + c2 = -2(ab + bc + ca)

3. a3 + b3 + c3 = -3ab(a + b)

Select the correct answer using the code given below.

1. 1 and 2 only
2. 2 and 3 only
3. 1 and 3 only
4. 1, 2 and 3

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selected

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

⇒ a+ b+ 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, a+ b+ c3 = 3abc

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

⇒ a+ b+ c3 = -3ab(a + b)

Option (3) is correct

Hence, 1, 2 and 3 are correct.