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\begin{document}

%%%%%%%%%%b{gedeonInfo}%%%%%%%%%
%%--Document N° 1445271706596--
%%--Ordre et comparaison--
%%%%%%%%%%e{gedeonInfo}%%%%%%%%%


\begin{exercise}
Comparer les nombres suivants:

\begin{enumerate}%
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\item $\frac{13}{14}$ et $\frac{14}{15}$

\item $8$ et $\sqrt{5} \times\sqrt{13}$

\item $\sqrt{17}+3\sqrt{2}$ et $\sqrt{19}+4$

\item $\sqrt{2}+\sqrt{3}$ et $\sqrt{5}$

\item $\sqrt{8}+\sqrt{6}$ et $\sqrt{12}+2$

\item $\sqrt{73+38\sqrt{3}}$ et $4\sqrt{3}+5$
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\end{enumerate}
\end{exercise}

\begin{exercise}
Soit $x$ un r\'{e}el tel que $\frac{9}{11}<x<\frac{6}{7}$.

Encadrer par des nombres rationnels puis par des nombres d\'{e}cimaux
comportant $2$ chiffres apr\`{e}s la virgule les r\'{e}els suivants:

\begin{enumerate}%
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\item $-3x+2$

\item $\frac{1}{x}$

\item $x^{2}$

\item $2-\frac{1}{x}$
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\end{enumerate}
\end{exercise}

\begin{exercise}
On consid\`{e}re $A=3+5\sqrt{2}$ et $B=\sqrt{58,99+30\sqrt{2}}$.

\begin{enumerate}
\item Calculer $A^{2}$ et $B^{2}$.

\item Comparer $A$ et $B$ puis $\frac{1}{A}$ et $\frac{1}{B}$ en invoquant un
r\'{e}sultat du cours.
\end{enumerate}
\end{exercise}

\begin{exercise}
On consid\`{e}re les nombres $A=5+2\sqrt{7}$ et $B=\sqrt{53+19\sqrt{7}}$.

\begin{enumerate}
\item Calculer $A^{2}$ et $B^{2}$.

\item Comparer $A$ et $B$.

\item Comparer $\frac{1}{A}$ et $\frac{1}{B}$.
\end{enumerate}
\end{exercise}

\begin{exercise}
Soient $a$ et $b$ deux nombres r\'{e}els positifs tels que $a\leqslant b$. Comparer:

\begin{enumerate}%
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\item $-5a+3$ et $-5b+3$

\item $(-3a^{2})$ et $(-3b^{2})$

\item $\frac{a}{b}$ et $\frac{b}{a}$

\item $2\sqrt{a}-11$ et $2\sqrt{b}-11$

\item $a+2b$ et $2a+b$

\item $\frac{1}{1+a^{2}}$ et $\frac{1}{1+b^{2}}$

\item $a^{2}+b^{2}$ et $(a+b)^{2}$

\item $\sqrt{a}+\sqrt{b}$ et $\sqrt{a+b}$%
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\end{enumerate}
\end{exercise}


\end{document}