1.

If a2 + b2 + c2 = 2(6a – 8b + 12c) – 244 so find the value of a + b + c.1. 122. 143. 104. 8

Answer» 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


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