Question

If the arithmetic mean of two distinct positive real numbers \(a\) and \(b\) (where \(a>b\)) is twice their geometric mean, then \(a : b\) is:

• A. \(2 + \sqrt{3} : 2 - \sqrt{3}\)
• B. \(2 + \sqrt{5} : 2 - \sqrt{5}\)
• C. \(2 + \sqrt{2} : 2 - \sqrt{2}\)
• D. None of these

Hint:

For problems involving means, always test edge cases and simplify radical expressions to find recognizable patterns.