Question

Find three numbers in G. P. whose sum is 38 and
whose product is 1728.​

Answer 1

Let the terms be a/r, a and ar.

So the product will be,

(a/r) a (ar) = 1728

a³ = 1728

a = 12

And the sum will be,

(a/r) + a + (ar) = 38

a [1/r + 1 + r] = 38

1/r + 1 + r = 19 / 6

1/r + r = 13 / 6

(r² + 1) / r = 13 / 6

6r² - 13r + 6 = 0

6r² - 9r - 4r + 6 = 0

3r(2r - 3) - 2(2r - 3) = 0

(2r - 3)(3r - 2) = 0

=> r = 3/2 or r = 2/3

Well, we get the same three terms whatever the value of r is.

So the three terms are 8, 12, 18.