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