If A and G be A.M. and GM., respectively between two positive numbers, prove that the numbers are `A+-sqrt((A+G)(A-G))`.

Explanation

To prove that the two positive numbers \( a \) and \( b \) can be expressed as \( A \pm \sqrt{(A + G)(A - G)} \), where \( A \) is the arithmetic mean (A.M.) and \( G \) is the geometric mean (G.M.) of \( a \) and \( b \), we will follow these steps:

### Step 1: Define A.M. and G.M.
Let the two positive numbers be \( a \) and \( b \). The arithmetic mean \( A \) and geometric mean \( G \) are defined as:
\[ A = \frac{a + b}{2} \]
\[
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