# Minimization Generalization

Geometry Level 3

I've seen a couple of variants of problem where we are to minimize a function which is a sum of square roots. Let's generalize a solution!

Let $$f(x,y)=\sqrt{(x+a)^2+(y+b)^2}+\sqrt{(x-c)^2+(y-d)^2}$$ for fixed $$a$$, $$b$$, $$c$$ and $$d$$.

The function $$f$$ has a global minimum which can be expressed as $$\sqrt{p(a,b,c,d)}$$ where $$p$$ is a polynomial over $$\mathbb{N}$$. Find the sum of the coefficients of $$p$$.

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