If a+b+c=0, then which of the following are correct? 1. a^{3}+b^{3}+c^{3}=3abc 2. a^{2}+b^{2}+c^{2}=-2(ab+bc+ca) 3. a^{3}+b^{3}+c^{3}=-3ab(a+b) Select the correct answer using the code given below.
- A. 1 and 2 only
- B. 2 and 3 only
- C. 1 and 3 only
- D. 1, 2 and 3 ✓
Correct Answer: D. 1, 2 and 3
Explanation
Statement 1 is a standard identity for a+b+c=0. Statement 2 follows from (a+b+c)^2 = 0. Statement 3 is true because c = -(a+b), substituting this into 3abc yields -3ab(a+b). All are correct.
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