L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Soit \( X=\left(-\dfrac{41}{8}\right)\sqrt{63}\) et \( Y=\left(\left(-\dfrac{14}{3}\right)\sqrt{28}\right)-\left(\left(\dfrac{73}{9}\right)\sqrt{175}\right)-\left(\left(\left(-\dfrac{1}{2}\right)\sqrt{63}\right)-\left(\left(-\dfrac{34}{3}\right)\sqrt{63}\right)\right)-\left(\left(\left(\dfrac{29}{9}\right)\sqrt{49}\right)-\dfrac{10}{7}\right)\) . 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{41}{8}\right)\sqrt{63}\right)+\left(\left(\left(-\dfrac{14}{3}\right)\sqrt{28}\right)-\left(\left(\dfrac{73}{9}\right)\sqrt{175}\right)-\left(\left(\left(-\dfrac{1}{2}\right)\sqrt{63}\right)-\left(\left(-\dfrac{34}{3}\right)\sqrt{63}\right)\right)-\left(\left(\left(\dfrac{29}{9}\right)\sqrt{49}\right)-\dfrac{10}{7}\right)\right)\\
&=&\left(\left(-\dfrac{123}{8}\right)\sqrt{7}\right)+\left(\left(\left(-\dfrac{28}{3}\right)\sqrt{7}\right)-\left(\left(\dfrac{365}{9}\right)\sqrt{7}\right)-\left(\left(\left(-\dfrac{3}{2}\right)\sqrt{7}\right)-\left(\left(-34\right)\sqrt{7}\right)\right)-\left(\dfrac{203}{9}-\dfrac{10}{7}\right)\right)\\
&=&\left(-\dfrac{123}{8}\right)\sqrt{7}+\left(\left(-\dfrac{28}{3}\right)\sqrt{7}\right)-\left(\left(\dfrac{365}{9}\right)\sqrt{7}\right)-\left(\left(\left(-\dfrac{3}{2}\right)\sqrt{7}\right)-\left(\left(-34\right)\sqrt{7}\right)\right)-\left(\dfrac{203}{9}-\dfrac{10}{7}\right)\\
&=&\left(-\dfrac{7039}{72}\right)\sqrt{7}-\dfrac{1331}{63}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(-\dfrac{41}{8}\right)\sqrt{63}\right)-\left(\left(\left(-\dfrac{14}{3}\right)\sqrt{28}\right)-\left(\left(\dfrac{73}{9}\right)\sqrt{175}\right)-\left(\left(\left(-\dfrac{1}{2}\right)\sqrt{63}\right)-\left(\left(-\dfrac{34}{3}\right)\sqrt{63}\right)\right)-\left(\left(\left(\dfrac{29}{9}\right)\sqrt{49}\right)-\dfrac{10}{7}\right)\right)\\
&=&\left(\left(-\dfrac{123}{8}\right)\sqrt{7}\right)-\left(\left(\left(-\dfrac{28}{3}\right)\sqrt{7}\right)-\left(\left(\dfrac{365}{9}\right)\sqrt{7}\right)-\left(\left(\left(-\dfrac{3}{2}\right)\sqrt{7}\right)-\left(\left(-34\right)\sqrt{7}\right)\right)-\left(\dfrac{203}{9}-\dfrac{10}{7}\right)\right)\\
&=&\left(\left(-\dfrac{123}{8}\right)\sqrt{7}\right)-\left(\left(-\dfrac{1483}{18}\right)\sqrt{7}-\dfrac{1331}{63}\right)\\
&=&\left(-\dfrac{123}{8}\right)\sqrt{7}+\left(\dfrac{1483}{18}\right)\sqrt{7}+\dfrac{1331}{63}\\
&=&\left(\dfrac{4825}{72}\right)\sqrt{7}+\dfrac{1331}{63}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(-\dfrac{41}{8}\right)\sqrt{63}\right)\times\left(\left(\left(-\dfrac{14}{3}\right)\sqrt{28}\right)-\left(\left(\dfrac{73}{9}\right)\sqrt{175}\right)-\left(\left(\left(-\dfrac{1}{2}\right)\sqrt{63}\right)-\left(\left(-\dfrac{34}{3}\right)\sqrt{63}\right)\right)-\left(\left(\left(\dfrac{29}{9}\right)\sqrt{49}\right)-\dfrac{10}{7}\right)\right)\\
&=&\left(\left(-\dfrac{123}{8}\right)\sqrt{7}\right)\times\left(\left(\left(-\dfrac{28}{3}\right)\sqrt{7}\right)-\left(\left(\dfrac{365}{9}\right)\sqrt{7}\right)-\left(\left(\left(-\dfrac{3}{2}\right)\sqrt{7}\right)-\left(\left(-34\right)\sqrt{7}\right)\right)-\left(\dfrac{203}{9}-\dfrac{10}{7}\right)\right)\\
&=&\left(\left(-\dfrac{123}{8}\right)\sqrt{7}\right)\left(\left(-\dfrac{1483}{18}\right)\sqrt{7}-\dfrac{1331}{63}\right)\\
&=&\left(\dfrac{60803}{48}\right)\sqrt{49}+\left(\dfrac{54571}{168}\right)\sqrt{7}\\
&=&\dfrac{425621}{48}+\left(\dfrac{54571}{168}\right)\sqrt{7}\\
\end{eqnarray*}