# Summing Extremena

Algebra Level 5

Let $$f(x)=x^2-2ax-a^2-3/4$$. Let $$X$$ be the sum of the largest and smallest $$a$$ for which $$|f(x)| \leq 1$$ for all $$x \in [0, 1]$$. If $$X$$ can be expressed as $$\dfrac{\sqrt{n}-m}{p}$$, then find $$m+n+p$$.

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