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There are two pairs (x,y) of real numbers that satisfy the equation x + y = 3, xy = 1. Given that the solutions x are in the form x = (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 ?

 Feb 15, 2022
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By the quadratic formula, the solutions are x = (5 \pm 2*sqrt(5))/2, so a + b + c + d = 12.

 Feb 15, 2022

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