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There are two pairs $(x,y)$ of real numbers that satisfy the equation $x+y = 3xy = 5$. Given that the solutions $x$ are in the form $x = \frac{a \pm b\sqrt{c}}{d}$ where a, b, c, and d are positive integers and the expression is completely simplified, what is the value of a + b + c + d?

 Aug 26, 2021
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a + b + c + d = 124.

 Aug 26, 2021

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