What is the value of a3 + b3 + c3 if (a + b + c) = 0?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 3abc.
Given that
the value of a3 + b3 + c3
if (a + b + c) = 0
⇒ a + b = - c
Cube on both sides
⇒ a3 + 3a2b + 3ab2 + b3 = -c3
⇒ a3 + b3 + c3 + 3ab(a + b) = 0
Put value of a + b = -c
⇒ a3 + b3 + c3 - 3abc = 0
⇒ a3 + b3 + c3 = 3abc