Question

If a² + b² + c² = 2(6a – 8b + 12c) – 244 so find the value of a + b + c.

1. 12
2. 14
3. 10
4. 8

Answer 1

Correct Answer - Option 3 : 10

Given:

a² + b² + c² = 2(6a – 8b + 12c) – 244

Formula used:

(x + y)² = x² + y² + 2xy

(x – y)² = x² + y² – 2xy

Calculation:

a² + b² + c² = 2(6a – 8b + 12c) – 244

⇒ a² + b² + c² = 12a – 16b + 24c – 244

⇒ a² + b² + c² – 12a + 16b – 24c + 244 = 0

⇒ a² – 12a +  b² +16b +  c²  – 24c + 244 = 0

⇒ a² – (2 × 6)a +  b² + (2 × 8)b +  c²  – (2 × 12) c + 244 = 0

For perfect square add and subtract y²  

⇒ a² – (2 × 6)a + 6² – 6² + b² + (2 × 8)b + 8² – 64 + c²  – (2 × 12) c + 12² – 12² + 244 = 0

⇒ (a – 6)² + (b + 8)² + (c – 12)² – 244 + 244 = 0

⇒ (a – 6)² + (b + 8)² + (c – 12)² = 0

Here,

a – 6 = 0

⇒ a = 6

b + 8 = 0

⇒ b = - 8

c – 12 = 0

⇒ c = 12

So, a + b + c

⇒ 6 – 8 + 12

⇒ 10

∴ The value of a + b + c is 10