Question

If a² + b² + c² + 170 = 2 (8a + 5b - 9c), then the value of \(\rm \sqrt {4a + 8b -c}\) will be:
1. 8
2. 12
3. 9
4. 15

Answer 1

Correct Answer - Option 3 : 9

Given:

a² + b² + c² + 170 = 2(8a + 5b - 9c)

Concept used :

a2 + b2 + 2ab = (a + b)²

a2 + b2 - 2ab = (a - b)²

Calculations:

a2 + b2 + c2 + 170 = 2(8a + 5b - 9c)

a2 + b2 + c2 - 16a - 10b + 18c + 170 = 0

a2 - 16a + 64 + b2 - 10b + 25 + c2 + 18c + 81 = 0 (∵ 64 + 25 + 81 = 170)

(a - 8)² + (b - 5)² + (c + 9)² = 0

Now,

(a - 8)2 = a - 8 = 0

⇒ a = 8, 

Similarly,

⇒ b = 5 & c = -9

Now,

⇒ √(4a + 8b - c) = [(32 + 40 - (- 9)]

⇒ √(72 + 9)
⇒ √81

⇒ 9

∴ The correct choice will be option 3.