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.

CDS 2021 PYQ with Answer — If a + b + c = 0, then which of the following are correct? 1. a³ + b³…

2021 · Q97

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

1a³ + b³ + c³ = 3abc;
2a² + b² + c² = −2(ab + bc + ca);
3a³ + b³ + c³ = −3ab(a + b).

Select the correct answer using the code given below.

Elementary MathematicsAlgebra

A1 and 2 only
B2 and 3 only
C1 and 3 only
D1, 2 and 3

Explanation

Statement 1: a³+b³+c³ − 3abc = (a+b+c)(a²+b²+c²−ab−bc−ca) = 0 — true. Statement 2: (a+b+c)² = 0 expands to a²+b²+c² = −2(ab+bc+ca) — true. Statement 3: since c = −(a+b), 3abc = −3ab(a+b) — true. All three are correct. Hence option D.