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Question
If a + 2b + c = 0; then show that a3 + 8b3 + c3 = 6abc
Solution
a + 2b + c = 0 ...(i)
⇒ (a + 2b) + c = 0
⇒ (a + 2b)3 + c3 + 3(a + 2b) c(a + 2b + c) = 0
⇒ a3 + 8b2 + 6ab (a + 2b) + c3 + 0 = 0
⇒ a3 + 8b3 + c3 + 6ab (a + 2b) = 0 ....(2)
Using (1), we get a + 2b = -c
From (2),
a3 + 8b3 + 6ab (-c) = 0
⇒ a3 + 8b3 + c3 = 6abc.
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