Find three numbers in G.P. whose product is 729 and the sum of their products in pairs is 819.

Question

Philoid · Accepted Answer

Let the three numbers be .

∴ According to the question

⇒ …(1)

From 1 we get

⇒ a³ = 729

∴ a = 9.

⇒

⇒ a + ar + a² = 819

Substituting a = 9 in above equation we get

⇒ 9 + 9r + 81 = 819

⇒ 9r = 729

⇒ r = 81

∴ are the three numbers.