3. Solve the inequality:

$$
x^{2}-2 x+3 \leqslant \sqrt{4-x^{2}}
$$
3. For the left side of the inequality, we have $x^{2}-2 x+3=\left(x^{2}-2 x+\right.$ 1) $+2=(x-1)^{2}+2 \geqslant 2$, and for the right side, we have $\sqrt{4-x^{2}} \leqslant \sqrt{4}=2$. Therefore, the only possibility is for both the left and right sides to be equal to 2. However, from the derivation above, we notice that the left side is equal to 2 only for $x=1$, and the right side is equal to 2 only for $x=0$. Thus, it is never possible for both sides to be simultaneously equal to 2, so the given inequality has no solution.