3. Given real numbers $x, y$ satisfy
$$
\left(x+\sqrt{x^{2}+2}\right)\left(y+\sqrt{y^{2}+4}\right)=16 .
$$

Then the value of $x \sqrt{y^{2}+4}+y \sqrt{x^{2}+2}$ is ( ).
(A) $\frac{27}{4}$.
(B) $\frac{29}{4}$
(C) $\frac{31}{4}$
(D) $\frac{33}{4}$
3. C.

From equation (1), we easily obtain
$$
\left(x-\sqrt{x^{2}+2}\right)\left(y-\sqrt{y^{2}+4}\right)=\frac{1}{2} \text {. }
$$

Expanding equations (1) and (2) respectively and then subtracting them, we get
$$
x \sqrt{y^{2}+4}+y \sqrt{x^{2}+2}=\frac{31}{4} .
$$