Question

The sum of three numbers in GP is 38 and their product is 1728. Find the numbers.

Answer 1

Let the numbers are a/r, a and ar
product = 1728
⇒ a/r * a * ar = 1728
⇒ a³ = 1728
⇒ a = 12

12/r + 12 + 12r = 38
⇒ 12 + 12r + 12r² = 38r
⇒ 12r² - 26r + 12 = 0
⇒ 6r² - 13r + 6 = 0
r = 2/3 and 3/2

when r = 2/3
numbers are 8, 12 and 18

when r = 3/2
the numbers are 18,12,8

the required numbers are 8, 12 and 18