% racines carrées
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%%%     Feuille d'exercices de mathématiques au format LaTeX     %%%
%%%     créée le Fri, 12 Sep 2008 00:45:14 +0200                 %%%
%%%     sur http://allken-bernard.org/pierre/phpmyexercices      %%%
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% Apparence des exercices
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\lhead{\textbf{\today}} 
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\rhead{\textbf{\thepage/\pageref{fin}}}
\lfoot{\small \textit{Lycée Joachim du Bellay}}
\cfoot{\small \textit{Mathématiques, prépa ECE1}}
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%%%     Exercice 99
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre l'équation suivante dans~$\bf R$~:
\[\sqrt{x+4}=4x+2\]
\end{exercice}


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%%%     Exercice 101
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre l'équation suivante dans~$\bf R$~:
\[\sqrt{x^2-3x+8}=x-4\]
\end{exercice}


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%%%     Exercice 102
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre l'équation suivante dans~$\bf R$~:
\[\sqrt{2x^2+x-6}=x+2\]
\end{exercice}


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%%%     Exercice 103
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre l'équation suivante en fonction du paramètre~$m$~:
\[\sqrt{4x^2-9}=2x-m\]
\end{exercice}


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%%%     Exercice 104
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre l'équation~:
\[\sqrt{4+\sqrt{x^4+x^2}}=x-2\]
\end{exercice}


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%%%     Exercice 105
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre l'équation~:
\[\sqrt{4+\sqrt{x^4+x^2}}=2-x\]
\end{exercice}


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%%%     Exercice 113
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre~:
\[\sqrt{x-3}+1>0\]
\end{exercice}


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%%%     Exercice 114
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre~:
\[\sqrt{x+6}>\sqrt{21-2x}\]
\end{exercice}


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%%%     Exercice 115
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre~:
\[\sqrt{x-2}>x-5\]
\end{exercice}


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%%%     Exercice 116
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre~:
\[\sqrt{x-1}+\sqrt{x-2}=1\]
\end{exercice}


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%%%     Exercice 117
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre~:
\[\sqrt{2x-5}-\sqrt{x-3}>1\]
\end{exercice}


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%%%     Exercice 118
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre~:
\[\sqrt{x^2+x+4}>3\]
\end{exercice}


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%%%     Exercice 119
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre~:
\[x^2-3x+\sqrt{x^2-3x+11}=1\]
\end{exercice}


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%%%     Exercice 120
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]On veut calculer~:
\[S=\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\cdots+\frac{1}{\sqrt{99}+\sqrt{100}}\]
\begin{enumerate}
\item Calculer $(\sqrt{x}+\sqrt{x+1})(\sqrt{x}-\sqrt{x+1})$.
\item En déduire une autre expression pour $\dfrac{1}{\sqrt{x}+\sqrt{x+1}}$.
\item Calculer $S$.
\end{enumerate}
\end{exercice}


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%%%     Exercice 121
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]En supposant que le nombre~:
\[\alpha=\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\cdots}}}}}\]
ait un sens, combien vaut-il~?
\end{exercice}

\label{fin}
\end{document}