Đề bài

Tìm số nguyên thích hợp điền vào chỗ chấm (…): a) \(\frac{{ - 12}}{{19}} < \frac{{...}}{{19}} < \frac{{...}}{{19}} < \frac{{...}}{{19}} < \frac{{ - 8}}{{19}}\) b) \(\frac{{ - 1}}{2} < \frac{{...}}{{24}} < \frac{{...}}{{12}} < \frac{{...}}{8} < \frac{{ - 1}}{3}\)

Lời giải chi tiết

a) Đặt: \(\frac{{ - 12}}{{19}} < \frac{x}{{19}} < \frac{y}{{19}} < \frac{z}{{19}} < \frac{{ - 8}}{{19}}\)\(\begin{array}{l} \Rightarrow  - 12 < x < y < z <  - 8\\ \Rightarrow \left\{ \begin{array}{l}x =  - 11\\y =  - 10\\z =  - 9\end{array} \right.\end{array}\)Vậy \(\frac{{ - 12}}{{19}} < \frac{{ - 11}}{{19}} < \frac{{ - 10}}{{19}} < \frac{{ - 9}}{{19}} < \frac{{ - 8}}{{19}}\) b) Đặt \(\frac{{ - 1}}{2} < \frac{x}{{24}} < \frac{y}{{12}} < \frac{z}{8} < \frac{{ - 1}}{3}\)\(\begin{array}{l} \Leftrightarrow \frac{{ - 12}}{{24}} < \frac{x}{{24}} < \frac{{2y}}{{24}} < \frac{{3z}}{{24}} < \frac{{ - 8}}{{24}}\\ \Leftrightarrow  - 12 < x < 2y < 3z <  - 8\\ \Leftrightarrow \left\{ \begin{array}{l}x =  - 11\\2y =  - 10\\3z =  - 9\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}x =  - 11\\y =  - 5\\z =  - 3\end{array} \right.\end{array}\)