Question

If p, q, r are in AP, then p³ + r³ - 8q³ is equal to ______.

Options

• 4pqr

• -6pqr

• 2pqr

• 8pqr

Answer 1

If p, q, r are in AP, then p³ + r³ - 8q³ is equal to -6pqr.

Explanation:-

∵ p, q, r are in AP.

∴ 2q = p + r

⇒ p + r – 2q = 0

∴ p³ + r³ + (-2p)³ = 3 × p × r × -2q [Using if a + 6 + c = 0 ⇒ a³ + b³ + c³ = 3 abc]

⇒ p³ + r³ - 8q³ = -6pqr.