If a2 + b2 = 14, and a + b = 4. Find a3 - b31. 14√32. 12√23. 30

1.	If a2 + b2 = 14, and a + b = 4. Find a3 - b31. 14√32. 12√23. 30√34. 21√2
Answer» Correct Answer - Option 3 : 30√3 Given: a2 + b2 = 14 a + b = 4 Formula Used: (a + b)² = a² + b² + 2ab (a - b)2 = a2 + b2 - 2ab a³ - b³ = (a - b)(a² + b² + ab) Calculation: (4)² = 14 + 2ab ⇒ 16 - 14 = 2ab ⇒ ab = 2/2 = 1 (a - b)² = 14 - 2 × 1 ⇒ (a - b) = 2√3 a3 - b3 = (2√3)(14 + 1) ⇒ a3 - b3 = 30√3 ∴ The value of a3 - b³ is 30√3.

If a2 + b2 = 14, and a + b = 4. Find a3 - b31. 14√32. 12√23. 30√34. 21√2

Answer» Correct Answer - Option 3 : 30√3

Given:

a2 + b2 = 14

a + b = 4

Formula Used:

(a + b)² = a² + b² + 2ab

(a - b)2 = a2 + b2 - 2ab

a³ - b³ = (a - b)(a² + b² + ab)

Calculation:

(4)² = 14 + 2ab

⇒ 16 - 14 = 2ab

⇒ ab = 2/2 = 1

(a - b)² = 14 - 2 × 1

⇒ (a - b) = 2√3

a3 - b3 = (2√3)(14 + 1)

⇒ a3 - b3 = 30√3

∴ The value of a3 - b³ is 30√3.

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If a2 + b2 = 14, and a + b = 4. Find a3 - b31. 14√32. 12√23. 30√34. 21√2

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