3. The minimum value of the algebraic expression $113 \sqrt{x^{2}+3}-110 x$ is . $\qquad$
$3.3 \sqrt{223}$.
Let $y=113 \sqrt{x^{2}+3}-110 x$, then $y^{2}+220 x y=3 \times 223 x^{2}+3 \times 113^{2}$,
which means $3 \times 223 x^{2}-220 y x+3 \times 113^{2}-y^{2}=0$.
Thus, $\Delta=(200 y)^{2}-4 \times 3 \times 223\left(3 \times 113^{2}-y^{2}\right)$
$$
=4 \times 113^{2}\left(y^{2}-3^{2} \times 223\right) \geqslant 0 \text {. }
$$

Therefore, $y \geqslant 3 \sqrt{223}$.
When and only when $x=\frac{110}{\sqrt{223}}$, $y$ reaches its minimum value $3 \sqrt{223}$.