Question

If 2(2m + 3n) = 11 and mn = 1, then find the value of 16m² - 36n²?
1. ± 22
2. ± 44
3. ± 55
4. ± 65

Answer 1

Correct Answer - Option 3 : ± 55

Given:

2(2m + 3n) = 11

⇒ 4m + 6n = 11

mn = 1

Formula used:

(a - b)² = (a + b)² - 4ab

a² - b² = (a + b)(a - b)

Calculation:

∵ (4m - 6n)² = (4m + 6n)² - 4 × (4m)(6n)

= (11)2 - (4 × 24 × mn)

= 121 - 96

= 25

∴ 4m - 6n = ±√25

= ± 5

∴ 16m2 - 36n2 = (4m - 6n) × (4m + 6n)

= (± 5) × (11)

= ± 55