9.072. $x^{8}-6 x^{7}+9 x^{6}-x^{2}+6 x-9<0$.

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9.072. $x^{8}-6 x^{7}+9 x^{6}-x^{2}+6 x-9<0$.
Solution.

Rewrite the inequality as

$$
\begin{aligned}
& x^{6}\left(x^{2}-6 x+9\right)-\left(x^{2}-6 x+9\right)0 \quad \text{and} \quad x^{2}-x+1>0 \quad \text{for} \quad x \in \mathbb{R}, \text{so it is equivalent to the inequality} \quad (x-3)^{2}(x-1)(x+1)<0. \text{Using the interval method, we get} \quad x \in(-1 ; 1).

![](https://cdn.mathpix.com/cropped/2024_05_22_fa9db84b44b98ec0a5c7g-543.jpg?height=126&width=610&top_left_y=621&top_left_x=363)

Answer: \quad x \in(-1 ; 1)
$$