L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Soit \( X=\left(-\dfrac{20}{3}\right)\sqrt{50}-\dfrac{79}{6}-\left(\left(-\dfrac{13}{8}\right)\sqrt{18}\right)-\left(\left(6\right)\sqrt{4}\right)-\left(\left(\dfrac{77}{5}\right)\sqrt{18}\right)+\left(\dfrac{21}{2}\right)\sqrt{8}+\left(-\dfrac{7}{8}\right)\sqrt{4}\) et \( Y=\left(-\dfrac{41}{7}\right)\sqrt{4}\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(\left(-\dfrac{20}{3}\right)\sqrt{50}-\dfrac{79}{6}-\left(\left(-\dfrac{13}{8}\right)\sqrt{18}\right)-\left(\left(6\right)\sqrt{4}\right)-\left(\left(\dfrac{77}{5}\right)\sqrt{18}\right)+\left(\dfrac{21}{2}\right)\sqrt{8}+\left(-\dfrac{7}{8}\right)\sqrt{4}\right)+\left(\left(-\dfrac{41}{7}\right)\sqrt{4}\right)\\
&=&\left(\left(-\dfrac{100}{3}\right)\sqrt{2}-\dfrac{79}{6}-\left(\left(-\dfrac{39}{8}\right)\sqrt{2}\right)-12-\left(\left(\dfrac{231}{5}\right)\sqrt{2}\right)+\left(21\right)\sqrt{2}-\dfrac{7}{4}\right)+\left(-\dfrac{82}{7}\right)\\
&=&\left(-\dfrac{100}{3}\right)\sqrt{2}-\dfrac{79}{6}-\left(\left(-\dfrac{39}{8}\right)\sqrt{2}\right)-12-\left(\left(\dfrac{231}{5}\right)\sqrt{2}\right)+\left(21\right)\sqrt{2}-\dfrac{7}{4}-\dfrac{82}{7}\\
&=&\left(-\dfrac{6439}{120}\right)\sqrt{2}-\dfrac{3245}{84}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(-\dfrac{20}{3}\right)\sqrt{50}-\dfrac{79}{6}-\left(\left(-\dfrac{13}{8}\right)\sqrt{18}\right)-\left(\left(6\right)\sqrt{4}\right)-\left(\left(\dfrac{77}{5}\right)\sqrt{18}\right)+\left(\dfrac{21}{2}\right)\sqrt{8}+\left(-\dfrac{7}{8}\right)\sqrt{4}\right)-\left(\left(-\dfrac{41}{7}\right)\sqrt{4}\right)\\
&=&\left(\left(-\dfrac{100}{3}\right)\sqrt{2}-\dfrac{79}{6}-\left(\left(-\dfrac{39}{8}\right)\sqrt{2}\right)-12-\left(\left(\dfrac{231}{5}\right)\sqrt{2}\right)+\left(21\right)\sqrt{2}-\dfrac{7}{4}\right)-\left(-\dfrac{82}{7}\right)\\
&=&\left(\left(-\dfrac{6439}{120}\right)\sqrt{2}-\dfrac{323}{12}\right)-\left(-\dfrac{82}{7}\right)\\
&=&\left(-\dfrac{6439}{120}\right)\sqrt{2}-\dfrac{323}{12}+\dfrac{82}{7}\\
&=&\left(-\dfrac{6439}{120}\right)\sqrt{2}-\dfrac{1277}{84}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(-\dfrac{20}{3}\right)\sqrt{50}-\dfrac{79}{6}-\left(\left(-\dfrac{13}{8}\right)\sqrt{18}\right)-\left(\left(6\right)\sqrt{4}\right)-\left(\left(\dfrac{77}{5}\right)\sqrt{18}\right)+\left(\dfrac{21}{2}\right)\sqrt{8}+\left(-\dfrac{7}{8}\right)\sqrt{4}\right)\times\left(\left(-\dfrac{41}{7}\right)\sqrt{4}\right)\\
&=&\left(\left(-\dfrac{100}{3}\right)\sqrt{2}-\dfrac{79}{6}-\left(\left(-\dfrac{39}{8}\right)\sqrt{2}\right)-12-\left(\left(\dfrac{231}{5}\right)\sqrt{2}\right)+\left(21\right)\sqrt{2}-\dfrac{7}{4}\right)\times\left(-\dfrac{82}{7}\right)\\
&=&\left(\left(-\dfrac{6439}{120}\right)\sqrt{2}-\dfrac{323}{12}\right)\left(-\dfrac{82}{7}\right)\\
&=&\left(\dfrac{263999}{420}\right)\sqrt{2}+\dfrac{13243}{42}\\
&=&\left(\dfrac{263999}{420}\right)\sqrt{2}+\dfrac{13243}{42}\\
\end{eqnarray*}