1. a) Solve the inequality $x^{4}-2 x^{3}-4 x^{2}>6-5 x$.

b) Solve the equation $x^{6}-5 x^{3}=14$.
1. 

a) We solve the inequality $x^{4}-2 x^{3}-4 x^{2}+5 x-6>0$. We solve the equation $x^{4}-2 x^{3}-4 x^{2}+5 x-6=0$ and write down the real solutions of the equation $x_{1}=-2$ and $x_{2}=3$. We write the solution of the inequality $x \in(-\infty,-2) \cup(3, \infty)$.

b) We solve the equation $x^{6}-5 x^{3}-14=0$ and factorize it as $\left(x^{3}-7\right)\left(x^{3}+2\right)=0$. We write the real solutions of the equation $x_{1}=\sqrt[3]{7}$ and $x_{2}=-\sqrt[3]{2}$.

a) Solving the inequality $x^{4}-2 x^{3}-4 x^{2}+5 x-6>0 \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots$

Solving the equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $1^{*}$ point

![](https://cdn.mathpix.com/cropped/2024_06_07_115a7be78276e1d4adcag-18.jpg?height=52&width=1676&top_left_y=882&top_left_x=230)

![](https://cdn.mathpix.com/cropped/2024_06_07_115a7be78276e1d4adcag-18.jpg?height=51&width=1676&top_left_y=934&top_left_x=230)

![](https://cdn.mathpix.com/cropped/2024_06_07_115a7be78276e1d4adcag-18.jpg?height=60&width=1739&top_left_y=1009&top_left_x=176)

![](https://cdn.mathpix.com/cropped/2024_06_07_115a7be78276e1d4adcag-18.jpg?height=51&width=1676&top_left_y=1068&top_left_x=230)

Solving the equation $x^{3}-7=0$ and the first solution $x_{1}=\sqrt[3]{7} \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots$

Solving the equation $x^{3}+2=0$ and the second solution $x_{2}=-\sqrt[3]{2} \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots$ point