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Question
If a + 2b + c = 0; then show that: a3 + 8b3 + c3 = 6abc.
Sum
Solution
Given that a + 2b + c = 0
∴ a + 2b = -c ...(1)
Now consider the expansion of (a + 2b)3
(a + 2b)3 = (-c)3
⇒ a3 + (2b)3 + 3 × a × 2b × (a + 2b) = (-c)3
⇒ a3 + 8b3 + 3 × a × 2b × (-c) = (-c)3 ...[From (1)]
⇒ a3 + 8b3 - 6abc = -c3
⇒ a3 + 8b3 + c3 = 6abc
Hence, proved.
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