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Question
If 3a + 5b + 4c = 0, show that : 27a3 + 125b3 + 64c3 = 180 abc
Solution
Given that 3a + 5b + 4c = 0
3a + 5b = - 4c
Cubing both sides,
(3a + 5b)3 = (-4c)3
⇒ (3a)3 + (5b)3 + 3 x 3a x 5b (3a + 5b) = -64c3
⇒ 27a3 + 125b3 + 45ab x (-4c) = -64c3
⇒ 27a3 + 125b3 - 180abc = -64c3
⇒ 27a3 + 125b3 + 64c3 = 180abc
Hence proved.
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