# What's C, G, and N?

Algebra Level 4

Let $$C$$ be the answer to this problem.
Let $$G$$ be the answer to this problem.
Let $$N$$ be the answer to this problem.

Let $$m$$ be the largest root of $$x^3 + Cx^2 + Gx - N = 0$$. $$m$$ can be written as $$\sqrt{a} - \sqrt{b}$$, where $$a,b$$ are positive integers. What is the value of $$a+b$$?

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