If A and G are the arithmetic and geometric means respectively of two numbers then prove that the numbers are `(A+sqrt(A^(2)-G^(2)))and(A-sqrt(A^(2)-G^(2)))`

Explanation

To prove that the two numbers whose arithmetic mean is \( A \) and geometric mean is \( G \) are given by \( A + \sqrt{A^2 - G^2} \) and \( A - \sqrt{A^2 - G^2} \), we can follow these steps:

### Step 1: Define the Arithmetic and Geometric Means
Let the two numbers be \( x \) and \( y \). The arithmetic mean \( A \) and geometric mean \( G \) are defined as:
\[ A = \frac{x + y}{2} \]
\[
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