সমাধান করুনঃ ∛(1 + a) + ∛(1 - a) = ∛2

প্রশ্নঃ সমাধান করুনঃ ∛(1 + a) + ∛(1 - a) = ∛2

সমাধানঃ
∛(1 + a) + ∛(1 - a) = ∛2
⇒ {∛(1 + a) + ∛(1 - a)}³ = (∛2)³ [ ঘন করে ]
⇒ {∛(1 + a)}³ + {∛(1 - a)}³ + 3 . ∛(1 + a) . ∛(1 - a) . {∛(1 + a) + ∛(1 - a)} = 2
⇒ 1 + a + 1 - a + 3 . (1 + a)^1/3 . (1 - a)^1/3 {∛2} = 2 [ যেহেতু, ∛(1 + a) + ∛(1 - a) = ∛2]
⇒ 2 + 3 (1 + a)^1/3 . (1 - a)^1/3 . 2^1/3 = 2
⇒ 3 (1 + a)^1/3 . (1 - a)^1/3 . 2^1/3 = 0
⇒ (1 + a)^1/3 . (1 - a)^1/3 = 0
⇒ (1 + a) (1 - a) = 0

হয়, 1 + a = 0
বা, a = - 1

অথবা,
1 - a = 0
বা, a = 1

∴ a = 1, -1