Tìm

- Hướng dẫn giải

1. $\mathrm{P}=\frac{1,5\mathrm{n}}{\mathrm{n}+10}$ là phân số

$$\begin{gathered} \iff \left\{\begin{array}{l}1,5.\mathrm{n}\in \mathrm{\mathbb{Z}}\\ \mathrm{n}+10\in \mathrm{\mathbb{Z}}\\ \mathrm{n}+10\ne 0\end{array}\right. \\ \iff \left\{\begin{array}{l}\mathrm{n} \mathrm{là}\mathrm{số}\mathrm{nguyên}\mathrm{chẵn}\\ \mathrm{n}\ne 10\end{array}\right. \end{gathered}$$

2. Ta có:

$\begin{array}{l}\mathrm{P}=\frac{7}{8}\iff \frac{1,5.\mathrm{n}}{\mathrm{n}+10}=\frac{7}{8}\\ \iff 8.1,5.\mathrm{n}=7(\mathrm{n}+10)\\ \iff 12.\mathrm{n}=7\mathrm{n}+70\\ \iff 12\mathrm{n}-7\mathrm{n}=70\\ \iff 5\mathrm{n}=70\\ \iff \mathrm{n}=14\end{array}$