1957 AHSME Problems/Problem 36
Problem
If 
, then the largest value of 
is:
Solution
By AM-GM, we have
![\[\frac{x+y}{2} \geq \sqrt{xy}\]](http://latex.artofproblemsolving.com/9/9/f/99fa58a672272e2c58e856e035838fac36cebf3c.png)
Substituting, we have
![\[\frac{1}{2} \geq \sqrt {xy}\]](http://latex.artofproblemsolving.com/6/f/0/6f01cae884790a11d14890d3c93664d1ae1d09c1.png)
![\[\frac{1}{4} \geq xy\]](http://latex.artofproblemsolving.com/4/b/6/4b68740b10f0fb21e2e2b88bb702de8e9bc17869.png)
Equality occurs when 
.
~JustinLee2017
See Also
| 1957 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 35 |
Followed by Problem 37 | |
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| All AHSME Problems and Solutions | ||
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