# An algebra problem by Julian Yu

Algebra Level 5

Let $$a$$, $$b$$, and $$c$$ be real numbers such that $$a+b+c=2$$ and $${a}^{2}+{b}^{2}+{c}^{2}=12$$.

If the difference between the maximum and minimum values of $$c$$ can be expressed as $$\dfrac{p}{q}$$, where $$p$$ and $$q$$ are coprime positive integers, find $$p+q$$.

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