Question

If a + 2b + c = 0; then show that: a³ + 8b³ + c³ = 6abc.

Answer 1

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.