If a + 2b + c = 0; then show that :

a³ + 8b³ + c³ = 6abc.

Given,

a + 2b + c = 0 ……..(1)

By property,

If x + y + z = 0, then

⇒ x³ + y³ + z³ = 3xyz ………(2)

Comparing,

Eq. 1 with x + y + z = 0, we get :

x = a, y = 2b and z = c.

Then,

Substituting value of x, y and z in Eq. 2, we get :

⇒ a³ + (2b)³ + c³ = 3 × a × 2b × c

⇒ a³ + 8b³ + c³ = 6abc.

Hence, proved that a³ + 8b³ + c³ = 6abc.