Question

Cel mai mare numar intreg mai mic sau egal cu 3+ 1/rad3 - 3 este

3+ 1 supra radical din 3 - 3

Answer 1

$\\ Avem numarul 3+\dfrac{1}{\sqrt3-3},\quad pornim de la inecuatia 1\ \textless \ \sqrt3\ \textless \ 2. \\ \\ \\ 1\ \textless \ \sqrt3\ \textless \ 2 \Big|-3 \\ \\ -2\ \textless \ \sqrt3-3\ \textless \ -1\Big|^{-1} \\ \\ \dfrac{1}{-2}\ \textgreater \ \dfrac{1}{\sqrt3-3}\ \textgreater \ \dfrac{1}{-1} \\ \\ -\dfrac{1}{2}\ \textgreater \ \dfrac{1}{\sqrt3-3}\ \textgreater \ -1\Big|+3 \\ \\ -\dfrac{1}{2}+3\ \textgreater \ \dfrac{1}{\sqrt3-3}+3\ \textgreater \ 2$
$2\ \textless \ \dfrac{1}{\sqrt3-3}+3\ \textless \ -\dfrac{1}{2}+3 \\ \\ 2\ \textless \ 3+\dfrac{1}{\sqrt3-3}\ \textless \ 2,5\quad \quad (ne intereseaza doar de 2) \\ \\ \Rightarrow cel mai mare numar intreg mai mic decat 3+\dfrac{1}{\sqrt3-3} este 2.$