Almost Vieta's

Algebra Level 5

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

Let aa, bb and cc be real numbers such that the system of equations above is true. If the sum of the minimum and maximum values of cc can be written in the form xy\frac{x}{y}, where xx and yy are coprime positive integers, find x+yx+y.

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