Question

Aratati ca 2<sau=ab/5<sau=abc/50,pt.orice nr nat de forma abc.

Answer 1

$\overline{ab} \geq 10 \Rightarrow \frac{\overline{ab}}{5} \geq \frac{10}{5}=2.~~~~~~~~~(1) \\ \overline{abc} \geq \overline{ab0} \Rightarrow \frac{\overline{abc}}{50} \geq \frac{\overline{ab0}}{50}= \frac{\overline{ab}*10}{50}= \frac{\overline{ab}}{5}.~~~~~~~~~(2) \\ \\ Din~(1)~si~(2),~rezulta~2 \leq \frac{\overline{ab}}{5} \leq \frac{\overline{abc}}{50}.$