Question

Din jumatatea unui numar rational se scade numarul 0,(2), rezultatul se tripleaza si se obtine numarul 2,3(6).
Determinati numarul necunoscut.

Answer 1

  [tex]*\\0,(2)=\frac{2}{9}\;;\;2,3(6)=\frac{236-23}{90}=\frac{213^{(3}}{90}=\frac{71}{30}\;;\\ **\\ (\frac{x}{2}-\frac{2}{9})\cdot3=\frac{71}{30}\;\Leftrightarrow\;\frac{9x-4}{18}\cdot3=\frac{71}{30}\,\Leftrightarrow\,\frac{9x-4}{6}=\frac{71}{30}\\ 30(9x-4)=6\cdot71\;|_{:6}\;\Leftrightarrow \;45x-20=71\;deci\;\fbox{x=91/45}[/tex]