If the A.M. of two positive numbers `aa n db(a > b)` is twice their geometric mean. Prove that : `a : b=(2+sqrt(3)):(2-sqrt(3))dot`

Explanation

To prove that if the arithmetic mean (A.M.) of two positive numbers \( a \) and \( b \) (where \( a > b \)) is twice their geometric mean (G.M.), then the ratio \( a : b = (2 + \sqrt{3}) : (2 - \sqrt{3}) \), we can follow these steps:

### Step 1: Write the relationship between A.M. and G.M.
The arithmetic mean of \( a \) and \( b \) is given by:
\[ \text{A.M.} = \frac{a + b}{2} \]
The geometric mean of \( a \) and \( b \) is given by:
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