# Is there an elegant method?

Geometry Level 5

Let the line $$y-\sqrt{3}x+3=0$$ intersect the parabola $$2y^{2}=2x+3$$ at points $$A$$ and $$B$$.

Find $$|PA-PB|$$, where $$P$$ is the point $$(\sqrt{3},0)$$ and $$PA$$ represents the length of line segment ends at $$P$$ and $$A$$.


Notation: $$| \cdot |$$ denotes the absolute value function.

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