If a + b + c = 6 and a2 + b2 + c2 = 14, then what is the value of (a - b)2 + (b − c)2 + (c - a)2?
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Correct answer: D
Explanation
The correct answer is Option 4 i.e. 6.
We know that,
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
⇒ (6)2 = 14 + 2(ab + bc + ca)
⇒ ab + bc + ca = 11
Now (a - b)2 + (b − c)2 + (c- a)2 = a2 + b2 - 2ab + b2 + c2 + c2 + a2 - 2ac
⇒ 2(a2 + b2 + c2) - 2(ab + bc + ca)
⇒ 2(14) - 2(11)
⇒ 28 - 22 = 6