If a2 + b2 + 49 c2 + 18 = 2 (b - 28c - a) then the value of (a + b - 7c) is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 4.
⇒ a2 + b2 + 49 c2 + 18 = 2 (b - 28c - a)
⇒ a2 + b2 + 49 c2 - 2b + 56c + 2a + 18 = 0
⇒ a2 + b2 + 49 c2 - 2b + 56c + 2a + 18 = 0
⇒ (a2 + 2a + 1) + (b2 - 2b + 1) + (49 c2 + 56c + 16) = 0
⇒ (a + 1)2 + (b - 1)2 + (7c + 4)2 = 0
a = -1, b = 1, c = -4/7
So, (a + b - 7c) = (-1 + 1 + 7 × 4/7)
= 4