Question

If a - b = 4 and ab = 21, find the value of a³ - b³
1. 302
2. 316
3. 304
4. 296

Answer 1

Correct Answer - Option 2 : 316

Given:

a - b = 4 and ab = 21

Formula Used:

a² + b² = (a - b)² + 2ab

a³ - b³ = (a - b)(a² + b² + ab)

Calculation:

As, a - b = 4 and ab = 21

Now, a2 + b2 = (4)2 + 2 × 21 = 16 + 42 = 58

a3 - b3 = (4)(58 + 21) = 4 × 79 = 316

∴ The value of a3 - b³ is 316.