Question
Download Solution PDFIf (a3 + b3 + c3 - 3abc) = 405, and (a + b + c) = 15, find the value of (a - b)2 + (b - c)2+(c - a)2.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
(a3 + b3 + c3 - 3abc) = 405, and (a + b + c) = 15
Concept used:
(a3 + b3 + c3 - 3abc) = 1/2 (a + b + c) [(a - b)2 + (b - c)2+(c - a)2]
Calculation:
(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. = 810 / 15
⇒ (a - b)2 + (b - c)2+(c - a)2 = 54
∴ The correct option is 2
Last updated on Jul 21, 2025
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