Question

The sum of three numbers in ap is 12 and sum of their cubes is 288

Answer 1

Answer:

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Answer 2

• Let three numbers be (a - d), a, (a + d).

» The sum of three numbers in ap is 12.

→ a - d + a + a + d = 12

→ 3a = 12

→ a = 4

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» Sum (let numbers) of their cubes is 288.

→ (a - d)³ + (a)³ + (a + d)³ = 288

(a + b)³ = a³ + b³ + 3a²b + 3ab²

(a - b)³ = a³ - b³ - 3a²b + 3ab²

→ a³ + d³ + 3a²d + 3ad² + a³ + a³ - d³ - 3a²d + 3ad² = 288

→ 3a³ + 6ad² = 288

→ 3(4)³ + 6(4)d² = 288

→ 192 + 24d² = 288

→ 24d² = 96

→ d² = 4

→ d = ±2

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Now..

› Take a = 4 and d = - 2

• (a - d) = 4 - (-2) = 4 + 2

=> 6

• a = 4

• (a + d) = 4 + (-2) = 4 - 2

=> 2

› Take a = 4 and d = +2

• (a + d) = 4 + 2

=> 6

• a = 4

• (a - d) = 4 - 2

=> 2

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A.P : 2, 4, 6 or 6, 4, 2

_______ [ ANSWER ]

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