# Logarithm Sums

Algebra Level 3

$$x$$ and $$y$$ are positive real numbers that satisfy $$\log_x y + \log_y x = \frac{17}{4}$$ and $$xy = 288\sqrt{3}$$. If $$x + y = a + b\sqrt{c}$$, where $$a$$, $$b$$ and $$c$$ are positive integers and $$c$$ is not divisible by the square of any prime, what is the value of $$a + b + c$$?

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