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1957 AHSME Problems/Problem 36

By AM-GM, we have \[\frac{x+y}{2} \geq \sqrt{xy}\] Substituting, we have \[\frac{1}{2} \geq \sqrt {xy}\] \[\frac{1}{4} \geq xy\] Equality occurs when $x = y = \frac{1}{2}$ $\boxed{D}$

~JustinLee2017

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