Question

The sum of three numbers in G.P. is `39/10` and their product is 1. Find the numbers.

Answer 1

Let the number be `a/r`, a and ar.

`=> a/r xx a xx ar = 1`

`=>` a³ = 1

`=>` a = 1

Now, `a/r + a + ar = 39/10`

`=> 1/r + 1 + r = 39/10`

`=> (1 + r + r^2)/r = 39/10`

`=>` 10 + 10r + 10r² = 39r

`=>` 10r² – 29r + 10 = 0

`=>` 10r² – 25r – 4r + 10 = 0

`=>` 5r(2r – 5) – 2(2r – 5) = 0

`=>` (2r – 5)(5r – 2) = 0

`=> r = 5/2` or `r = 2/5`

Thus, required terms are :

`a/r, a, ar = 1/(5/2), 1, 1 xx 5/2` or `1/(2/5), 1, 1 xx 2/5`

= `2/5, 1, 5/2` or `5/2, 1, 2/5`