3. The number of solutions to the equation $\left|x^{2}-1\right|=(4-2 \sqrt{3})(x+2)$ is ().
(A) 1
(B) 2
(C) 3
(D) 4
3. C.

When $|x| \geqslant 1$, the equation is
$$
x^{2}-1=(4-2 \sqrt{3})(x+2) \text {. }
$$

Solving it, we get $x_{1}=\sqrt{3}, x_{2}=4-3 \sqrt{3}$, both satisfying
$$
|x| \geqslant 1 \text {. }
$$

When $|x|<1$, the equation is
$$
1-x^{2}=(4-2 \sqrt{3})(x+2) \text {. }
$$

Solving it, we get $x_{3}=\sqrt{3}-2$, satisfying $|x|<1$.
In summary, the original equation has 3 solutions.