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if the line y=xsqrt3 cuts the curve x^3+...

if the line `y=xsqrt3` cuts the curve `x^3+y^3+3xy+5x^2+3y^2+4x+5y+1=0` at point `A,B,C` then find the value of `OA.OB.OC` is equal to (where `O` is the origin)

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To solve the problem, we need to find the value of \( OA \cdot OB \cdot OC \), where \( O \) is the origin and \( A, B, C \) are the points where the line \( y = x \sqrt{3} \) intersects the curve given by the equation: \[ x^3 + y^3 + 3xy + 5x^2 + 3y^2 + 4x + 5y + 1 = 0 \] ### Step 1: Substitute the line equation into the curve equation ...
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