L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Soit \( X=\left(\left(-\dfrac{61}{4}\right)\sqrt{175}\right)-\left(\left(\left(-\dfrac{79}{7}\right)\sqrt{49}\right)-\left(\left(-\dfrac{11}{8}\right)\sqrt{28}\right)-\left(\left(-9\right)\sqrt{175}\right)-\left(\left(-\dfrac{61}{4}\right)\sqrt{175}\right)\right)-\left(\left(\left(\dfrac{62}{7}\right)\sqrt{28}\right)-\dfrac{31}{3}\right)\) et \( Y=-1\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(\left(\left(-\dfrac{61}{4}\right)\sqrt{175}\right)-\left(\left(\left(-\dfrac{79}{7}\right)\sqrt{49}\right)-\left(\left(-\dfrac{11}{8}\right)\sqrt{28}\right)-\left(\left(-9\right)\sqrt{175}\right)-\left(\left(-\dfrac{61}{4}\right)\sqrt{175}\right)\right)-\left(\left(\left(\dfrac{62}{7}\right)\sqrt{28}\right)-\dfrac{31}{3}\right)\right)+\left(-1\right)\\
&=&\left(\left(\left(-\dfrac{305}{4}\right)\sqrt{7}\right)-\left(-79-\left(\left(-\dfrac{11}{4}\right)\sqrt{7}\right)-\left(\left(-45\right)\sqrt{7}\right)-\left(\left(-\dfrac{305}{4}\right)\sqrt{7}\right)\right)-\left(\left(\left(\dfrac{124}{7}\right)\sqrt{7}\right)-\dfrac{31}{3}\right)\right)+\left(-1\right)\\
&=&\left(\left(-\dfrac{305}{4}\right)\sqrt{7}\right)-\left(-79-\left(\left(-\dfrac{11}{4}\right)\sqrt{7}\right)-\left(\left(-45\right)\sqrt{7}\right)-\left(\left(-\dfrac{305}{4}\right)\sqrt{7}\right)\right)-\left(\left(\left(\dfrac{124}{7}\right)\sqrt{7}\right)-\dfrac{31}{3}\right)-1\\
&=&\left(-\dfrac{6103}{28}\right)\sqrt{7}+\dfrac{265}{3}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\left(-\dfrac{61}{4}\right)\sqrt{175}\right)-\left(\left(\left(-\dfrac{79}{7}\right)\sqrt{49}\right)-\left(\left(-\dfrac{11}{8}\right)\sqrt{28}\right)-\left(\left(-9\right)\sqrt{175}\right)-\left(\left(-\dfrac{61}{4}\right)\sqrt{175}\right)\right)-\left(\left(\left(\dfrac{62}{7}\right)\sqrt{28}\right)-\dfrac{31}{3}\right)\right)-\left(-1\right)\\
&=&\left(\left(\left(-\dfrac{305}{4}\right)\sqrt{7}\right)-\left(-79-\left(\left(-\dfrac{11}{4}\right)\sqrt{7}\right)-\left(\left(-45\right)\sqrt{7}\right)-\left(\left(-\dfrac{305}{4}\right)\sqrt{7}\right)\right)-\left(\left(\left(\dfrac{124}{7}\right)\sqrt{7}\right)-\dfrac{31}{3}\right)\right)-\left(-1\right)\\
&=&\left(\left(-\dfrac{6103}{28}\right)\sqrt{7}+\dfrac{268}{3}\right)-\left(-1\right)\\
&=&\left(-\dfrac{6103}{28}\right)\sqrt{7}+\dfrac{268}{3}+1\\
&=&\left(-\dfrac{6103}{28}\right)\sqrt{7}+\dfrac{271}{3}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\left(-\dfrac{61}{4}\right)\sqrt{175}\right)-\left(\left(\left(-\dfrac{79}{7}\right)\sqrt{49}\right)-\left(\left(-\dfrac{11}{8}\right)\sqrt{28}\right)-\left(\left(-9\right)\sqrt{175}\right)-\left(\left(-\dfrac{61}{4}\right)\sqrt{175}\right)\right)-\left(\left(\left(\dfrac{62}{7}\right)\sqrt{28}\right)-\dfrac{31}{3}\right)\right)\times\left(-1\right)\\
&=&\left(\left(\left(-\dfrac{305}{4}\right)\sqrt{7}\right)-\left(-79-\left(\left(-\dfrac{11}{4}\right)\sqrt{7}\right)-\left(\left(-45\right)\sqrt{7}\right)-\left(\left(-\dfrac{305}{4}\right)\sqrt{7}\right)\right)-\left(\left(\left(\dfrac{124}{7}\right)\sqrt{7}\right)-\dfrac{31}{3}\right)\right)\times\left(-1\right)\\
&=&\left(\left(-\dfrac{6103}{28}\right)\sqrt{7}+\dfrac{268}{3}\right)\left(-1\right)\\
&=&\left(\dfrac{6103}{28}\right)\sqrt{7}-\dfrac{268}{3}\\
&=&\left(\dfrac{6103}{28}\right)\sqrt{7}-\dfrac{268}{3}\\
\end{eqnarray*}