# Minimizing Inequality

Algebra Level 4

$\left(\dfrac{1}{1+2ab-c^2}+\dfrac{1}{1+2bc-a^2}+\dfrac{1}{1+2ca-b^2}\right)^2$

Let $$a,b$$ and $$c$$ be non-negative real numbers such that $$a^2+b^2+c^2=1$$.

The minimum value of the expression above can be expressed as $$\dfrac{p}{q}$$ for positive coprime integers $$p,q$$. Find $$p+q$$.

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