If \(\alpha,\beta,\gamma\) are the roots of the equation
\[
24x^3-10x^2-3x+1=0,
\]
then
\[
\frac{1}{\alpha^2}+\frac{1}{\beta^2}+\frac{1}{\gamma^2}
=
\]
Show Hint
For questions involving reciprocals of roots, first find
\(\alpha+\beta+\gamma\),
\(\alpha\beta+\beta\gamma+\gamma\alpha\),
and \(\alpha\beta\gamma\) using Vieta's formulas. Then express reciprocal sums in terms of these quantities.