Question

If a - b = 4 and a³ - b³ = 88, then find the value of a² - b².
1. \(8\sqrt{6}\)
2. \(6\sqrt{6}\)
3. \(7\sqrt{2}\)
4. \(9\sqrt{6}\)

Answer 1

Correct Answer - Option 1 : \(8\sqrt{6}\)

Given:

a - b = 4 and a³ - b³ = 88

Formula: ∴

(a³ - b³) = (a - b) (a² + b² + ab)

(a³ - b³) = (a - b) [(a - b)² + 3ab]

(a + b)² = a² + b² + 2ab

(a + b)(a - b) = a2 - b2

Calculation:

According to the formula

88 = 4 × (4² + 3ab)

⇒ 22 = 16 + 3ab

⇒ 3ab = 22 - 16

⇒ ab = 6/3

⇒ ab = 2

(a - b)² = a² + b² - 2ab

⇒ 4² = a² + b² - 2 × 2

⇒ a² + b² = 16 + 4 

⇒ a² + b² = 20

(a + b)² = 20 + 2 × 2

⇒ a + b = √24 = 2√6

Then (a + b)(a - b) = 2√6 × 4

⇒ 8√6 

∴ (a2 - b2) = 8√6