The sum of three numbers in G.P. is 21 and the sum of their squares is 189. Find the numbers.

Explanation

To solve the problem, we need to find three numbers in Geometric Progression (G.P.) such that their sum is 21 and the sum of their squares is 189. Let's denote the three numbers as \( a \), \( ar \), and \( ar^2 \), where \( a \) is the first term and \( r \) is the common ratio.

### Step 1: Set up the equations
From the problem, we have two equations based on the given conditions:

1. The sum of the numbers:
\[
a + ar + ar^2 = 21
...