L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Soit \( X=\left(-\dfrac{22}{7}\right)\sqrt{49}\) et \( Y=\left(\left(-\dfrac{12}{5}\right)\sqrt{175}\right)-\dfrac{69}{7}-\left(-\dfrac{17}{7}-\left(\left(-3\right)\sqrt{63}\right)-\left(\left(-\dfrac{79}{4}\right)\sqrt{63}\right)-\left(\left(\dfrac{31}{8}\right)\sqrt{175}\right)-\dfrac{77}{8}\right)-\left(\left(\dfrac{29}{3}\right)\sqrt{63}\right)\) . 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{22}{7}\right)\sqrt{49}\right)+\left(\left(\left(-\dfrac{12}{5}\right)\sqrt{175}\right)-\dfrac{69}{7}-\left(-\dfrac{17}{7}-\left(\left(-3\right)\sqrt{63}\right)-\left(\left(-\dfrac{79}{4}\right)\sqrt{63}\right)-\left(\left(\dfrac{31}{8}\right)\sqrt{175}\right)-\dfrac{77}{8}\right)-\left(\left(\dfrac{29}{3}\right)\sqrt{63}\right)\right)\\
&=&\left(-22\right)+\left(\left(\left(-12\right)\sqrt{7}\right)-\dfrac{69}{7}-\left(-\dfrac{17}{7}-\left(\left(-9\right)\sqrt{7}\right)-\left(\left(-\dfrac{237}{4}\right)\sqrt{7}\right)-\left(\left(\dfrac{155}{8}\right)\sqrt{7}\right)-\dfrac{77}{8}\right)-\left(\left(29\right)\sqrt{7}\right)\right)\\
&=&-22+\left(\left(-12\right)\sqrt{7}\right)-\dfrac{69}{7}-\left(-\dfrac{17}{7}-\left(\left(-9\right)\sqrt{7}\right)-\left(\left(-\dfrac{237}{4}\right)\sqrt{7}\right)-\left(\left(\dfrac{155}{8}\right)\sqrt{7}\right)-\dfrac{77}{8}\right)-\left(\left(29\right)\sqrt{7}\right)\\
&=&-\dfrac{1109}{56}+\left(-\dfrac{719}{8}\right)\sqrt{7}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(-\dfrac{22}{7}\right)\sqrt{49}\right)-\left(\left(\left(-\dfrac{12}{5}\right)\sqrt{175}\right)-\dfrac{69}{7}-\left(-\dfrac{17}{7}-\left(\left(-3\right)\sqrt{63}\right)-\left(\left(-\dfrac{79}{4}\right)\sqrt{63}\right)-\left(\left(\dfrac{31}{8}\right)\sqrt{175}\right)-\dfrac{77}{8}\right)-\left(\left(\dfrac{29}{3}\right)\sqrt{63}\right)\right)\\
&=&\left(-22\right)-\left(\left(\left(-12\right)\sqrt{7}\right)-\dfrac{69}{7}-\left(-\dfrac{17}{7}-\left(\left(-9\right)\sqrt{7}\right)-\left(\left(-\dfrac{237}{4}\right)\sqrt{7}\right)-\left(\left(\dfrac{155}{8}\right)\sqrt{7}\right)-\dfrac{77}{8}\right)-\left(\left(29\right)\sqrt{7}\right)\right)\\
&=&\left(-22\right)-\left(\left(-\dfrac{719}{8}\right)\sqrt{7}+\dfrac{123}{56}\right)\\
&=&-22+\left(\dfrac{719}{8}\right)\sqrt{7}-\dfrac{123}{56}\\
&=&-\dfrac{1355}{56}+\left(\dfrac{719}{8}\right)\sqrt{7}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(-\dfrac{22}{7}\right)\sqrt{49}\right)\times\left(\left(\left(-\dfrac{12}{5}\right)\sqrt{175}\right)-\dfrac{69}{7}-\left(-\dfrac{17}{7}-\left(\left(-3\right)\sqrt{63}\right)-\left(\left(-\dfrac{79}{4}\right)\sqrt{63}\right)-\left(\left(\dfrac{31}{8}\right)\sqrt{175}\right)-\dfrac{77}{8}\right)-\left(\left(\dfrac{29}{3}\right)\sqrt{63}\right)\right)\\
&=&\left(-22\right)\times\left(\left(\left(-12\right)\sqrt{7}\right)-\dfrac{69}{7}-\left(-\dfrac{17}{7}-\left(\left(-9\right)\sqrt{7}\right)-\left(\left(-\dfrac{237}{4}\right)\sqrt{7}\right)-\left(\left(\dfrac{155}{8}\right)\sqrt{7}\right)-\dfrac{77}{8}\right)-\left(\left(29\right)\sqrt{7}\right)\right)\\
&=&\left(-22\right)\left(\left(-\dfrac{719}{8}\right)\sqrt{7}+\dfrac{123}{56}\right)\\
&=&\left(\dfrac{7909}{4}\right)\sqrt{7}-\dfrac{1353}{28}\\
&=&\left(\dfrac{7909}{4}\right)\sqrt{7}-\dfrac{1353}{28}\\
\end{eqnarray*}