When axes are rotated through an angle \(\theta\) about the origin in the positive direction, if the equation
\[
3x^2+\sqrt{3}xy-5=0
\]
is transformed to the form
\[
ax'^2+by'^2=10,
\]
then \(ab=\)
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For rotation of axes,
\[
\boxed{AC-\left(\frac{B}{2}\right)^2}
\]
remains invariant. This invariant is often used to find the product of the transformed coefficients.