If a - b = 7 and a 2 + b 2 = 85, then find the value of a 3 - b 3 .

We know that, ⇒ (a - b) 2 = a 2 + b 2 - 2ab ⇒ (7) 2 = 85 - 2ab ⇒ 49 = 85 - 2ab ⇒ 2ab = 85 - 49 ⇒ 2ab = 36 ⇒ ab = 18. We know that, a 3 - b 3 = (a - b)(a 2 + b 2 + ab) Substituting values we get, ⇒ a 3 - b 3 = 7(85 + 18) = 7(103) = 721. Hence, a 3 - b 3 = 721.

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Mathematics

If a - b = 7 and a² + b² = 85, then find the value of a³ - b³.

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Answer

We know that,

⇒ (a - b)² = a² + b² - 2ab

⇒ (7)² = 85 - 2ab

⇒ 49 = 85 - 2ab

⇒ 2ab = 85 - 49

⇒ 2ab = 36

⇒ ab = 18.

We know that,

a³ - b³ = (a - b)(a² + b² + ab)

Substituting values we get,

⇒ a³ - b³ = 7(85 + 18) = 7(103) = 721.

Hence, a³ - b³ = 721.

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Mathematics

If a - b = 7 and a² + b² = 85, then find the value of a³ - b³.

Expansions

Answer

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Mathematics

If a - b = 7 and a2 + b2 = 85, then find the value of a3 - b3.

Expansions

Answer

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