Question

a³ – b³ = 5528, a – b = 8 then find (a – b)² + 3ab
1. 561
2. 661
3. 961
4. 691

Answer 1

Correct Answer - Option 4 : 691

Given:

a³ – b³ = 5528

a – b = 8

Formula used:

a³ – b³ = (a – b) (a² + ab + b²)

(a – b)² = a² + b² – 2ab

Calculation:

(a – b)² + 3ab = a² + b² – 2ab + 3ab

⇒ a² + ab + b²

(a³ – b³)/(a – b) = (a – b)(a² + ab + b²) / (a – b)

⇒ 5528/8

⇒ 691

∴ Required value is 691