Đáp án + giải thích các bước giải:

`(x^2-13)(x^2-17)<0`

`->`$\left\{\begin{matrix} x^2-13>0\\x^2-17<0 \end{matrix}\right.$

`->`$\left\{\begin{matrix} (x-\sqrt{13})(x+\sqrt{13})>0\\(x-\sqrt{17})(x+\sqrt{17})<0 \end{matrix}\right.$

`->`$\left\{\begin{matrix} \left[ \begin{array}{l}\left\{\begin{matrix} x-\sqrt{13}>0\\x+\sqrt{13}>0 \end{matrix}\right.\\\left\{\begin{matrix} x-\sqrt{13}<0\\x+\sqrt{13}<0 \end{matrix}\right.\end{array} \right.\\\left\{\begin{matrix} x+\sqrt{17}>0\\x-\sqrt{17}<0 \end{matrix}\right. \end{matrix}\right.$

`->`$\left\{\begin{matrix} \left[ \begin{array}{l}\left\{\begin{matrix} x>\sqrt{13}\\x>-\sqrt{13} \end{matrix}\right.\\\left\{\begin{matrix} x<\sqrt{13}\\x<-\sqrt{13} \end{matrix}\right.\end{array} \right.\\\left\{\begin{matrix} x>-\sqrt{17}\\x<\sqrt{17} \end{matrix}\right. \end{matrix}\right.$

`->`$\left\{\begin{matrix} \left[ \begin{array}{l}x>\sqrt{13}\\x<-\sqrt{13}\end{array} \right.\\-\sqrt{17}<x<\sqrt{17} \end{matrix}\right.$

`->`\(\left[ \begin{array}{l}-\sqrt{17}<x<-\sqrt{13}\\\sqrt{13}<x<\sqrt{17}\end{array} \right.\) 

Đáp án:

`(x^2 - 13)(x^2 - 17) < 0`

`⇒ x^2 - 13` và `x^2 - 17` trái dấu.

Mà `x^2 - 13 > x^2 - 17`

`⇒` $\left\{ \begin{array}{l}x^2 - 13 > 0\\x^2 - 17 < 0\end{array} \right.$

`⇒` $\left\{ \begin{array}{l}x^2 > 13\\x^2 < 17\end{array} \right.$

`⇒ 13 < x^2 < 17`

Mà `x ∈ ZZ` `⇒ 3 < x < 5`

`⇒ x = 4`  (TM)