Question

If 4a² + b² + 36c² + 6 = 2 (2a - b + 12c), then the value of (4a - 5b - 6c) is
1. 4
2. 5
3. 6
4. 7

Answer 1

Correct Answer - Option 2 : 5

Given:

4a² + b² + 36c² + 6 = 2 (2a - b + 12c)

Formula:

(a + b)² = a² + b² + 2ab

(a - b)² = a² + b² - 2ab

Calculations:

⇒ 4a² + b² + 36c² + 6 = 2 (2a - b + 12c)

⇒ 4a² + b² + 36c² + 6 = 4a - 2b + 24c

⇒ 4a² – 4a + b² + 2b + 36c² – 24c + 6 = 0

⇒ (4a² – 4a + 1) + (b² + 2b + 1) + (36c² – 24c + 4) = 0

⇒ (2a - 1)² + (b + 1)² + (6c - 2)² = 0

⇒ a = 1/2 

⇒ b = -1

⇒ c = 1/3

⇒ (4a - 5b - 6c) = 4(1/2) - 5(-1) – 6(1/3)

⇒ 7 - 2

⇒ 5

∴ the required answer is 5