Prove that a3 + 8b3 + 27c3 = 18 abc

If a + 2b + 3c = 0, Prove that a³ + 8b³ + 27c³ = 18 abc

Answer :

Given:

a + 2b + 3c = 0, a + 2b = – 3c

Let us cube on both the sides, we get

(a + 2b)³ = (-3c)³

a³ + (2b)³ + 3(a) (2b) (a + 2b) = -27c³

a³ + 8b³ + 6ab (– 3c) = – 27c³

a³ + 8b³ – 18abc = -27c³

a³ + 8b³ + 27c³ = 18abc

Hence proved.

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