Difference between revisions of "1964 AHSME Problems/Problem 37"
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==Problem== | ==Problem== | ||
− | Given two positive | + | Given two positive numbers <math>a</math>, <math>b</math> such that <math>a<b</math>. Let <math>A.M.</math> be their arithmetic mean and let <math>G.M.</math> be their positive geometric mean. Then <math>A.M.</math> minus <math>G.M.</math> is always less than: |
<math>\textbf{(A) }\dfrac{(b+a)^2}{ab}\qquad\textbf{(B) }\dfrac{(b+a)^2}{8b}\qquad\textbf{(C) }\dfrac{(b-a)^2}{ab}</math> | <math>\textbf{(A) }\dfrac{(b+a)^2}{ab}\qquad\textbf{(B) }\dfrac{(b+a)^2}{8b}\qquad\textbf{(C) }\dfrac{(b-a)^2}{ab}</math> |
Revision as of 18:45, 26 January 2021
Problem
Given two positive numbers , such that . Let be their arithmetic mean and let be their positive geometric mean. Then minus is always less than:
Solution
See Also
1964 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 36 |
Followed by Problem 38 | |
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All AHSME Problems and Solutions |
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