If a + b = 11 and a 2 + b 2 = 65; find a 3 + b 3 .

By formula, ⇒ (a + b) 2 = a 2 + b 2 + 2ab ⇒ 11 2 = 65 + 2ab ⇒ 121 = 65 + 2ab ⇒ 2ab = 56 ⇒ ab = = 28. By formula, ⇒ (a + b) 3 = a 3 + b 3 + 3ab(a + b) ⇒ 11 3 = a 3 + b 3 + 3 × 28 × 11 ⇒ 1331 = a 3 + b 3 + 924 ⇒ a 3 + b 3 = 1331 - 924 = 407. Hence, a 3 + b 3 = 407.

Mathematics

If a + b = 11 and a² + b² = 65; find a³ + b³.

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Answer

By formula,

⇒ (a + b)² = a² + b² + 2ab

⇒ 11² = 65 + 2ab

⇒ 121 = 65 + 2ab

⇒ 2ab = 56

⇒ ab = $\dfrac{56}{2}$ = 28.

By formula,

⇒ (a + b)³ = a³ + b³ + 3ab(a + b)

⇒ 11³ = a³ + b³ + 3 × 28 × 11

⇒ 1331 = a³ + b³ + 924

⇒ a³ + b³ = 1331 - 924 = 407.

Hence, a³ + b³ = 407.

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If a + b = 11 and a² + b² = 65; find a³ + b³.

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