3. Let $a$, $b$, $c$ be the roots of
$$
f(x)=x^{3}+3 x^{2}-10 x+5
$$

Then $a^{2} b^{2}+b^{2} c^{2}+c^{2} a^{2}=$ $\qquad$
3. 70 .

From the problem, we know
$$
\begin{array}{l}
a+b+c=-3, a b+b c+c a=-10, a b c=-5 . \\
\text { Therefore, } a^{2} b^{2}+b^{2} c^{2}+c^{2} a^{2} \\
=(a b+b c+c a)^{2}-2 a^{2} b c-2 b^{2} a c-2 c^{2} a b \\
=(a b+b c+c a)^{2}-2 a b c(a+b+c) \\
=70 .
\end{array}
$$