Difference between revisions of "1957 AHSME Problems/Problem 36"
(Created page with "By AM-GM, we have <cmath>\frac{x+y}{2} \geq \sqrt{xy}</cmath> Substituting, we have <cmath>\frac{1}{2} \geq \sqrt {xy}</cmath> <cmath>\frac{1}{4} \geq xy</cmath> Equality occu...") |
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Latest revision as of 20:31, 13 February 2021
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
