If `G_1` and `G_2` are two geometric means inserted between any two numbers and A is the arithmetic mean of two numbers, then the value of `(G_1^2)/G_2+(G_2^2)/G_1` is:

Explanation

To solve the problem, we need to find the value of the expression \(\frac{G_1^2}{G_2} + \frac{G_2^2}{G_1}\) where \(G_1\) and \(G_2\) are the geometric means inserted between two numbers \(a\) and \(b\), and \(A\) is their arithmetic mean.

### Step-by-Step Solution:

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