Find three numbers in G.P. whose sum is 65 and whose product is 3375.

Let the three numbers be .

∴ According to the question

⇒ …(1)

⇒ …(2)

From 2 we get,

⇒ a³ = 3375

∴ a = 15.

From 1 we get,

⇒

⇒ a + ar + ar² = 65r …(3)

Substituting a = 15 in 3 we get

⇒ 15 + 15r + 15r² = 65r

⇒ 15r² – 50r + 15 = 0…(4)

Dividing (4) by 5 we get

⇒ 3r² – 10r + 3 = 0

⇒ 3r² – 9r – r + 3 = 0

⇒ 3r(r – 3) – 1(r – 3) = 0

∴ r = 3 or r = 1/3

∴ Now the equation will be

⇒

⇒ 5,15,45 or 45,15,5.

∴ The three numbers are 5,15,45.