Difference between revisions of "1952 AHSME Problems/Problem 45"

(Created page with "== Problem == If <math>a</math> and <math>b</math> are two unequal positive numbers, then: <math>\text{(A) } \frac{2ab}{a+b}>\sqrt{ab}>\frac{a+b}{2}\qquad \text{(B) } \sqrt{ab...")
 
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== Solution ==
 
== Solution ==
<math>\fbox{C}</math>
+
Using the RMS-AM-GM-HM inequality, we can see that the answer is <math>\fbox{E}</math>
  
 
== See also ==
 
== See also ==

Revision as of 16:33, 9 July 2015

Problem

If $a$ and $b$ are two unequal positive numbers, then:

$\text{(A) } \frac{2ab}{a+b}>\sqrt{ab}>\frac{a+b}{2}\qquad \text{(B) } \sqrt{ab}>\frac{2ab}{a+b}>\frac{a+b}{2} \\ \text{(C) } \frac{2ab}{a+b}>\frac{a+b}{2}>\sqrt{ab}\qquad \text{(D) } \frac{a+b}{2}>\frac{2ab}{a+b}>\sqrt{ab} \\ \text{(E) } \frac {a + b}{2} > \sqrt {ab} > \frac {2ab}{a + b}$

Solution

Using the RMS-AM-GM-HM inequality, we can see that the answer is $\fbox{E}$

See also

1952 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 44
Followed by
Problem 46
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All AHSME Problems and Solutions

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