Determine [[$ \displaystyle\frac {1} {x} + \displaystyle\frac {1} {y} $]], when [[$ x + y = 52 $]] and [[$ xy = 13 $]]. (Finnish matriculation exam autumn 1995)

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Answer: [[$ \displaystyle\frac {1} {x} + \displaystyle\frac {1} {y} = $]]

Solution