The product of three numbers in G.P. is 125 and the sum of their products taken in pairs is . Find them.

Question

Philoid · Accepted Answer

Let the three numbers be .

∴ According to the question

⇒ …(1)

From 1 we get

⇒ a³ = 125

∴ a = 5.

⇒

⇒ a + ar + a² =

Substituting a = 5 in above equation we get

⇒ 5 + 5r + 25 =

⇒ 5r =

⇒

∴ are the three numbers.