1. |x| [tex]\leq[/tex] 3
2. -27 < x^3 [tex]\leq[/tex] 8
3. x^2 > 2 và x < 4
4. |x^2 - x| [tex]\leq[/tex] 2
5. 4 < x^2 < 16
Mong các anh chị giúp đỡ, em cảm ơn ạ
1.
$\Leftrightarrow -3\le x\le 3$
2.
$\Rightarrow \sqrt[3]{-27}<\sqrt[3]{x^3}<\sqrt[3]{8}\\\Leftrightarrow -3<x<2$
3.
$x^2>2\Rightarrow x>\sqrt 2\Rightarrow \sqrt 2<x<4$
4.
$\Leftrightarrow -2\le x^2-x\le 2$
*$x^2-x\ge -2 \Rightarrow x^2-x+2\ge 0$ luôn đúng với mọi $x$ (vì $x^2-x+2=\left(x-\dfrac 14\right)^2+\dfrac 74$)
*$x^2-x\le 2\\x^2-x-2\le 0\\(x+1)(x-2)\le 0$
TH1:
$
\left\{\begin{matrix}
x+1 \le 0\\
x-2 \ge 0
\end{matrix}\right. \Rightarrow \left\{\begin{matrix}
x\le -1\\
x\ge 2
\end{matrix}\right.\Rightarrow vô\ lí$
TH2:
$\left\{\begin{matrix}
x+1 \ge 0\\
x-2 \le 0
\end{matrix}\right. \Rightarrow \left\{\begin{matrix}
x\ge -1\\
x\le 2
\end{matrix}\right.\Rightarrow -1 \le x \le 2$
Vậy $-1 \le x \le 2$
5.
$\Rightarrow \sqrt{4}<\sqrt{x^2}<\sqrt{16}\\\Leftrightarrow 2<|x|<4\\\Rightarrow -4<x<-2 \ or \ 2<x<4$