Numar de patru cifre.

Marius Mainea · Post by **Marius Mainea** » Wed Dec 16, 2009 12:25 am

Determinati \( \overline{abcd} \) , \( a,c\neq 0 \) pentru care \( \frac{\sqrt{\overline{abcd}}}{\sqrt{\overline{ab}}+\sqrt{\overline{cd}}}\in\mathbb{Q} \).

Marius Mainea · Post by **Marius Mainea** » Tue Dec 29, 2009 5:47 pm

\( \sqrt{\overline{abcd}}\cdot\sqrt{\overline{ab}}\in\mathbb{Q} \) si \( \sqrt{\overline{abcd}}\cdot\sqrt{\overline{ab}}\in (\overline{ab0},\overline{ab5}) \)

Convine numai cazul \( \overline{abcd}\cdot\overline{ab}=\overline{ab4}^2 \) de unde \( \overline{abcd}=\overline{1681} \)

Mi se pare o demonstratie mai usoara decat cea de mai jos.

Andi Brojbeanu · Post by **Andi Brojbeanu** » Wed Dec 30, 2009 9:56 pm