If (a3 + b3 + c3 - 3abc) = 405, and (a - b)2 + (b - c)2 + (c - a)2 = 54, find the value of (a + b + c).
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 15.
We know,
(a3 + b3 + c3 - 3abc) = 1/2 × (a + b + c) × (a - b)2 + (b - c)2 + (c - a)2
According to the question;
⇒ 405 = (1/2) × (a + b + c) × 54
⇒ (a + b + c) = 810/54
⇒ (a + b + c) = 15