Mathematics
If a + 2b + 3c = 0, show that a3 + 8b3 + 27c3 = 18abc.
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Answer
We know that,
If x + y + z = 0 then x3 + y3 + z3 = 3xyz ……..(1)
Since, (a + 2b + 3c) = 0,
⇒ (a)3 + (2b)3 + (3c)3 = 3 × a × 2b × 3c
⇒ a3 + 8b3 + 27c3 = 18abc.
Hence, proved that a3 + 8b3 + 27c3 = 18abc.
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