3. Solve the inequality

$$
4 x+2+\sqrt{4-x}>x^{2}+\sqrt{x^{2}-5 x+2}
$$
# Problem 3.

Answer: $\left(2-\sqrt{6}, \frac{5-\sqrt{17}}{2}\right]$.

Solution. Rewrite the inequality as

$$
\sqrt{4-x}-\sqrt{x^{2}-5 x+2}>x^{2}-4 x-2
$$

then multiply and divide the left part by its conjugate expression:

$$
\begin{aligned}
& \frac{-\left(x^{2}-4 x-2\right)}{\sqrt{4-x}+\sqrt{x^{2}-5 x+2}}>x^{2}-4 x-2 \Longleftrightarrow\left(x^{2}-4 x-2\right)\left(\sqrt{4-x}+\sqrt{x^{2}-5 x+2}+1\right)<0 \\
& \Longleftrightarrow\left\{\begin{array}{l}
x^{2}-4 x-2<0, \\
4-x \geqslant 0, \\
x^{2}-5 x+2 \geqslant 0
\end{array} \Longleftrightarrow x \in\left(2-\sqrt{6}, \frac{5-\sqrt{17}}{2}\right]\right.
\end{aligned}
$$