% équations

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\lfoot{\small \textit{Lycée Joachim du Bellay}}
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%%%     Exercice 33
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%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre dans $\bf R$ l'équation~:
\[\frac{x-3}{2}-\frac{x-1}{3}=\frac{7x}{6}+\frac{2}{3}\]
\end{exercice}


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%%%     Exercice 34
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre dans $\bf R$ l'équation~:
\[\frac{6x-1}{5}-\frac{2x}{3}=\frac{x+1}{2}\]
\end{exercice}


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%%%     Exercice 35
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre dans $\bf R$ l'équation~:
\[(x+3)(2x-5)(6x+2)=0\]
\end{exercice}


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%%%     Exercice 36
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre dans $\bf R$ l'équation~:
\[x^2-11=0\]
\end{exercice}


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%%%     Exercice 38
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre dans $\bf R$ l'équation~:
\[(x+2)^2-(3x+4)^2=0\]
\end{exercice}


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%%%     Exercice 39
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre dans $\bf R$ l'équation~:
\[(x^2-4x+5)^2=(x^2+4x-13)^2\]
\end{exercice}


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%%%     Exercice 40
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre dans $\bf R$ l'équation~:
\[(x-1)^4+4(x+1)^3-(2x+1)(9x+2)+5x-19=0\]
\end{exercice}


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%%%     Exercice 41
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre dans $\bf R$ l'équation~:
\[\frac{3}{x-4}=\frac{2}{x+1}\]
\end{exercice}


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%%%     Exercice 42
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre dans $\bf R$ l'équation~:
\[\frac{2x+1}{x-3}=\frac{2x-1}{x+3}\]
\end{exercice}


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%%%     Exercice 43
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre dans $\bf R$ l'équation~:
\[\frac{x+2}{x-2}-\frac{x-2}{x+2}=\frac{8x}{x^2-4}\]
\end{exercice}


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%%%     Exercice 44
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre dans $\bf R$ l'équation~:
\[\frac{3}{x+3}-\frac{4}{x}=\frac{-x+2}{x^2+3x}\]
\end{exercice}


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%%%     Exercice 45
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre dans $\bf R$ l'équation~:
\[\frac{3-x}{3+x}-1=\frac{2-x}{2+x}+\frac{1-x}{1+x}\]
\end{exercice}


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%%%     Exercice 46
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre en fonction du paramètre $m$~:
\[(m+2)x+3m+1+\frac{m^2-6m}{2}x=\frac{7m}{2}\]
\end{exercice}


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%%%     Exercice 47
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre dans $\bf R$ l'équation~:
\[\frac{1}{1-\frac{x}{x-1}} + x =0\]
\end{exercice}


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%%%     Exercice 48
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre en fonction du paramètre $m$~:
\[m(mx+1)-7=3\left(3x-\frac{4}{3}\right)\]
\end{exercice}


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%%%     Exercice 49
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre en fonction du paramètre $m$~:
\[(2mx-3)^2=(x+m)^2\]
\end{exercice}


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%%%     Exercice 50
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre en fonction des paramètres $m$ et $p$~:
\[(x+m)^2-(x-p)^2=m+p\]
\end{exercice}


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%%%     Exercice 51
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre en fonction des paramètres $a$ et $b$~:
\[\frac{x}{a-b}+\frac{x}{a+b}=\frac{ab}{a^2-b^2}\]
\end{exercice}


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%%%     Exercice 53
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Soit~$\lambda\in\mathbf R$. Pour quelle(s) valeur(s) du paramètre~$m$ l'équation suivante admet-elle~$\lambda$ pour solution~?
\[\frac{2m}{x+2}=\frac{m-5}{x-1}\]
\end{exercice}


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%%%     Exercice 63
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre dans~$\bf R$~:
\[2x^2-9=0\]
\end{exercice}


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%%%     Exercice 64
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre dans~$\bf R$~:
\[-3x^2-2=0\]
\end{exercice}


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%%%     Exercice 65
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre dans~$\bf R$~:
\[(x-1)^2-6=0\]
\end{exercice}


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%%%     Exercice 66
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre dans~$\bf R$~:
\[x^2+12x+36=0\]
\end{exercice}


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%%%     Exercice 67
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre dans~$\bf R$~:
\[x^2+3x-10=0\]
\end{exercice}


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%%%     Exercice 68
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre dans~$\bf R$~:
\[x^2+7x-8=0\]
\end{exercice}


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%%%     Exercice 68
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre dans~$\bf R$~:
\[x^2+7x-8=0\]
\end{exercice}


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%%%     Exercice 69
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre dans~$\bf R$~:
\[\frac{1}{4}x^2-\frac{x}{5}+\frac{1}{25}=0\]
\end{exercice}


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%%%     Exercice 70
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre dans~$\bf R$~:
\[(3x-1)^2-(2x+3)^2=0\]
\end{exercice}


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%%%     Exercice 71
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre dans~$\bf R$~:
\[x^2-2x-120=0\]
\end{exercice}


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%%%     Exercice 72
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre dans~$\bf R$~:
\[(5x-3)^2-2(x+1)(15x-9)=0\]
\end{exercice}


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%%%     Exercice 73
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre dans~$\bf R$~:
\[x^2+(1+\sqrt 2)x+\sqrt 2=0\]
\end{exercice}


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%%%     Exercice 74
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre dans~$\bf R$~:
\[49x^2-28x+4=0\]
\end{exercice}


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%%%     Exercice 75
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre dans~$\bf R$~:
\[5x^2+x-1=0\]
\end{exercice}


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%%%     Exercice 76
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre dans~$\bf R$~:
\[5x^2-18x-35=0\]
\end{exercice}


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%%%     Exercice 77
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre dans~$\bf R$~:
\[\frac{5x+1}{x-3}=\frac{3x+4}{x+1}\]
\end{exercice}


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%%%     Exercice 78
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre dans~$\bf R$~:
\[(x-3)(2x+1)=(x-5)(x-7)+(x-2)^2+4-x\]
\end{exercice}


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%%%     Exercice 79
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Résoudre dans~$\bf R$~:
\[\frac{1}{x+1}+\frac{2}{x+2}+\frac{3}{x+3}=\frac{6}{x+4}\]
\end{exercice}


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%%%     Exercice 80
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Donner, en fonction du paramètre~$m$, le nombre de solutions de l'équation suivante.
\[(m-2)x^2+2(m+1)x+m-14=0\]
\end{exercice}


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%%%     Exercice 81
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Donner, en fonction du paramètre~$m$, le nombre de solutions de l'équation suivante.
\[(m+3)x^2-(2m-1)x+m+4=0\]
\end{exercice}


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%%%     Exercice 82
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Donner, en fonction du paramètre~$m$, le nombre de solutions de l'équation suivante.
\[x^2-2(m+3)x+m^2+2m-3=0\]
\end{exercice}


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%%%     Exercice 83
%%%     Le numéro correspond à la base de données :
%%%     http://allken-bernard.org/pierre/phpmyexercices                  
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\begin{exercice}
\nopagebreak[5]Montrer que l'équation $5x^2+12x-7=0$ admet deux solutions $x_1$ et $x_2$, sans les calculer.
\begin{enumerate}
\item Donner les valeurs de $x_1+x_2$ et de $x_1 x_2$.
\item En déduire $\frac{1}{x_1}+\frac{1}{x_2}$.
\item Calculer $x_1^2+x_2^2$ (indication~: calculer $(x_1+x_2)^2$ de deux façons).
\item Calculer $x_1^3+x_2^3$.
\item Calculer $\frac{1}{x_1+3}+\frac{1}{x_2+3}$.
\end{enumerate} 
\end{exercice}


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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 100
%%%     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~$\bf R$~:
\[x-\sqrt{x-5}=7\]
\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}

\label{fin}
\end{document}