# Almost Vieta's

Algebra Level 5

$\begin{cases} a+b+c =10\\ ab+bc+ca=25 \end{cases}$

Let $$a$$, $$b$$ and $$c$$ be real numbers such that the system of equations above is true. If the sum of the minimum and maximum values of $$c$$ can be written in the form $$\frac{x}{y}$$, where $$x$$ and $$y$$ are coprime positive integers, find $$x+y$$.

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