Difference between revisions of "1953 AHSME Problems/Problem 45"
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− | + | ==Problem== | |
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+ | The lengths of two line segments are <math>a</math> units and <math>b</math> units respectively. Then the correct relation between them is: | ||
+ | |||
+ | <math>\textbf{(A)}\ \frac{a+b}{2} > \sqrt{ab} \qquad | ||
+ | \textbf{(B)}\ \frac{a+b}{2} < \sqrt{ab} \qquad | ||
+ | \textbf{(C)}\ \frac{a+b}{2}=\sqrt{ab}\\ \textbf{(D)}\ \frac{a+b}{2}\leq\sqrt{ab}\qquad | ||
+ | \textbf{(E)}\ \frac{a+b}{2}\geq\sqrt{ab} </math> | ||
+ | |||
+ | ==Solution== | ||
+ | |||
+ | Since both lengths are positive, the [[AM-GM Inequality]] is satisfied. The correct relationship between <math>a</math> and <math>b</math> is <math>\boxed{\textbf{(E)}\ \frac{a+b}{2}\geq\sqrt{ab}}</math>. | ||
+ | |||
+ | ==See Also== | ||
+ | |||
+ | {{AHSME 50p box|year=1953|num-b=44|num-a=46}} | ||
+ | |||
+ | {{MAA Notice}} |
Latest revision as of 23:02, 14 February 2020
Problem
The lengths of two line segments are units and units respectively. Then the correct relation between them is:
Solution
Since both lengths are positive, the AM-GM Inequality is satisfied. The correct relationship between and is .
See Also
1953 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 44 |
Followed by Problem 46 | |
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