If (a + b + c) = 17, and (a2 + b2 + c2) = 101, 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. 14.
(a - b)2 + (b - c)2 + (c - a)2
= a2 + b2 - 2ab + b2 + c2 - 2bc + c2 + a2 - 2ac
= 2(a2 + b2 + c2) - (2ab + 2bc + 2ac)
= 2(117) - [(a + b + c)2 - (a2 + b2 + c2)]
= 234 - [(17)2 - 117]
= 234 - (289 - 117)
= 234 - 172
= 62
Hence, the required value is 62.