If a = 101, b = 102 and c = 103, then a² + b² + c² - ab - bc - ca =
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 3.
We know that,
(a - b)2 + (b - c)2 + (c - a)2 = 2(a2 + b2 + c2 - ab - bc - ca)
given that, a = 101, b = 102, and c = 103
⇒ (101 - 102)2 + (102 - 103)2 + (103 - 101)2 = 2(a2 + b2 + c2 - ab - bc - ca)
⇒ 12 + 12 + 22 = 2(a2 + b2 + c2 - ab - bc - ca)
⇒ (1 + 1 + 4) = 2(a2 + b2 + c2 - ab - bc - ca)
⇒ 6/2 = (a2 + b2 + c2 - ab - bc - ca)
⇒ a2 + b2 + c2 - ab - bc - ca = 3