If a2 + b2 + 49c2 + 18 = 2(b - 28c - a), then the value of (a - b - 7c) is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 2.
a2 + b2 + 49c2 + 18 = 2(b - 28c - a)
⇒ a2 + b2 + 49c2 + 18 = 2b - 56c - 2a
⇒ a2 + b2 + 49c2 + 18 - 2b + 56c + 2a = 0
⇒ a2 + 2a + 1 + b2 - 2b + 1 + 49c2 + 56c + 16 = 0
⇒ (a + 1)2 + (b - 1)2 + (7c + 4)2 = 0
Now the above equation is 0, only when -
a + 1 = 0, b - 1 = 0, 7c + 4 = 0
a = - 1, b = 1, c = - 4/7
⇒ (a - b - 7c) = (-1) - (1) -7(-4/7) = -2 + 4 = 2