If (a3 + b3 + c3 - 3abc) = 405, and (a + b + c) = 15, find the value of (a - b)2 + (b - c)2 + (c - a)2.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 54.
We know that,
(a3 + b3 + c3 - 3abc) = 1/2 (a + b + c) [(a - b)2 + (b - c)2 + (c - a)2]
⇒ 405 = 1/2 × 15 [(a - b)2 + (b - c)2 + (c - a)2]
⇒ [(a - b)2 + (b - c)2 + (c - a)2] = (405 × 2)/15
⇒ [(a - b)2 + (b - c)2 + (c - a)2] = 27 × 2
⇒ [(a - b)2 + (b - c)2 + (c - a)2] = 54