Question:medium
If two positive numbers are in the ratio \( 3 + 2\sqrt{2} : 3 - 2\sqrt{2} \), then the ratio between their A.M. and G.M. is:
If two positive numbers are in the ratio \( 3 + 2\sqrt{2} : 3 - 2\sqrt{2} \), then the ratio between their A.M. and G.M. is:
Show Hint
If the ratio of two numbers is \( \frac{x + \sqrt{x^2 - 1}}{x - \sqrt{x^2 - 1}} \), the ratio of their A.M. to G.M. is always \( x : 1 \). Here, \( 3^2 - (2\sqrt{2})^2 = 1 \), so the ratio is \( 3 : 1 \).
Updated On: May 6, 2026
- \( 6 : 1 \)
- \( 3 : 2 \)
- \( 2 : 1 \)
- \( 3 : 1 \)
- \( 1 : 6 \)
Show Solution
The Correct Option is D
Solution and Explanation
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