Question

If 36a² + 64b² = 64 and ab = 2, then find the value of 6a + 8b.

1. 18
2. 19
3. 16
4. 21

Answer 1

Correct Answer - Option 3 : 16

Given:

36a² + 64b² = 64            

ab = 2

Formula used:

(a + b)² = a² + b² + 2ab

Calculation:

⇒ (6a + 8b)² = (6a)²  + (8b)² + 2 × 6a × 8b

⇒ 36a² + 64b² + 96 ab

⇒ 64 + 96 × 2 = 256

⇒ (6a + 8b)² = 256

⇒ (6a + 8b) = √256

⇒ 6a + 8b = 16

∴ The value of 6a + 8b is 16