Question

If a + b + c =0, then the value of a³ + b³ + c³ is.

1. ab
2. abc
3. 3abc
4. 4abc

Answer 1

Correct Answer - Option 3 : 3abc

Given Data:

a + b + c = 0

Formula Used:

a3+ b3 + c3 – 3abc = (a+b+c)( a2+ b2+c2 −ab−bc–ca)

Calculation:

According to the formula,

a³+ b³ + c³ – 3abc = (a + b + c)( a² + b² + c² − ab − bc – ca)

But (a+b+c) = 0

⇒ a³+ b³ + c³ – 3abc = 0

⇒ a³+ b³ + c³ = 3abc 

∴ a³ + b³ + c³ is 3abc.