If `A` be one A.M. and `p ,q` be two G.M. `' s` between two numbers, then `2A` is equal to (a)`(p^3+q^3)/(p q)` (b) `(p^3-q^3)/(p q)` (c) `(p^2+q^2)/2` (d) `(p q)/2`

Explanation

To solve the problem, we need to find the expression for \( 2A \) in terms of the two geometric means \( p \) and \( q \) between two numbers \( A \) and \( B \).

### Step-by-Step Solution:

1. **Understanding the Arithmetic Mean (A.M.)**:
The arithmetic mean \( A \) of two numbers \( A \) and \( B \) is given by:
\[
A = \frac{A + B}{2}
...