Question

If a² + b² = 82 and ab = 9, then a possible value of a³ + b³ is:
1. 750
2. 730
3. 830
4. 720

Answer 1

Correct Answer - Option 2 : 730

Given:

a² + b² = 82

ab = 9

Formula used:

(a + b)² = a² + b² + 2ab

(a + b)³ = a³ + b³ + 3ab(a + b)

Calculation:

(a + b)3 = a3 + b3 + 3ab(a + b)

We need to find (a + b)

(a + b)2 = a2 + b2 + 2ab

⇒ (a + b)² = 82 + 2 × 9

⇒ (a + b)² = 100

⇒ (a + b) = 10

Now,

(a + b)3 = a3 + b3 + 3ab(a + b)

⇒ (10)³ = a³ + b³ + 3 × 9 × 10

⇒ 1000 = a³ + b³ + 270

⇒ a³ + b³ = 1000 - 270 = 730

∴ the value of a³ + b³ is 730