If the line \( y-\sqrt{3} x+3=0 \) cuts the curve \( y^{2}=x+2 \) at \( A \) and \( B \), then f...

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If the line \( y-\sqrt{3} x+3=0 \) cuts the curve \( y^{2}=x+2 \) at \( A \) and \( B \), then find the value of \( P A \cdot P B \) where \( P \equiv(\sqrt{3}, 0)\} \)
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