The sum of three numbers in a G.P. is 38 and their product is 1728. Find the greatest number.Choices:- 18 10 20 22

Let's denote the three numbers as a/r, a, and ar. These are in geometric progression.

Given that the sum of the three numbers is 38, we can write the equation:

a/r + a + ar = 38

Given that the product of the three numbers is 1728, we can write the equation:

(a/r) * a * ar = 1728

Solving these two equations, we get:

a^3 = 1728, so a = 12 (since 12^3 = 1728)

Substituting a = 12 into the first equation, we get:

12/r + 12 + 12r = 38

Solving this equation for r, we get two roots: r = 1/2 and r = 2.

So, the three numbers are 6 (when r = 1/2), 12 (when r = 1), and 24 (when r = 2).

Therefore, the greatest number is 24, which is not in the given choices.