Summing Extremena

Algebra Level 5

Let f(x)=x22axa23/4f(x)=x^2-2ax-a^2-3/4. Let XX be the sum of the largest and smallest aa for which f(x)1|f(x)| \leq 1 for all x[0,1]x \in [0, 1]. If XX can be expressed as nmp\dfrac{\sqrt{n}-m}{p}, then find m+n+pm+n+p.

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