# Difference between revisions of "1964 AHSME Problems/Problem 37"

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==Problem== | ==Problem== | ||

− | Given two positive number <math>a</math>, <math>b</math> such that <math>a<b</math>. Let A.M. be their arithmetic mean and let | + | Given two positive number <math>a</math>, <math>b</math> such that <math>a<b</math>. Let A.M. be their arithmetic mean and let G.M. be their positive geometric mean. Then A.M. minus G.M. 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{(D) }\dfrac{(b-a)^2}{8a}\qquad \textbf{(E) }\dfrac{(b-a)^2}{8b}</math> |

## Revision as of 17:21, 5 March 2014

## Problem

Given two positive number , such that . Let A.M. be their arithmetic mean and let G.M. be their positive geometric mean. Then A.M. minus G.M. is always less than: