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