L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Soit \( X=\left(9\right)\sqrt{63}+\dfrac{73}{3}+\left(-\dfrac{16}{3}\right)\sqrt{28}+\left(-\dfrac{59}{8}\right)\sqrt{175}+\left(\dfrac{34}{3}\right)\sqrt{49}+\left(\left(8\right)\sqrt{49}\right)-\left(\left(-\dfrac{19}{4}\right)\sqrt{28}\right)-\left(\left(8\right)\sqrt{49}\right)+\left(\left(-\dfrac{52}{9}\right)\sqrt{175}\right)-\left(\left(\dfrac{75}{7}\right)\sqrt{175}\right)\) et \( Y=\left(-\dfrac{32}{9}\right)\sqrt{49}\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(\left(9\right)\sqrt{63}+\dfrac{73}{3}+\left(-\dfrac{16}{3}\right)\sqrt{28}+\left(-\dfrac{59}{8}\right)\sqrt{175}+\left(\dfrac{34}{3}\right)\sqrt{49}+\left(\left(8\right)\sqrt{49}\right)-\left(\left(-\dfrac{19}{4}\right)\sqrt{28}\right)-\left(\left(8\right)\sqrt{49}\right)+\left(\left(-\dfrac{52}{9}\right)\sqrt{175}\right)-\left(\left(\dfrac{75}{7}\right)\sqrt{175}\right)\right)+\left(\left(-\dfrac{32}{9}\right)\sqrt{49}\right)\\
&=&\left(\left(27\right)\sqrt{7}+\dfrac{73}{3}+\left(-\dfrac{32}{3}\right)\sqrt{7}+\left(-\dfrac{295}{8}\right)\sqrt{7}+\dfrac{238}{3}+56-\left(\left(-\dfrac{19}{2}\right)\sqrt{7}\right)-56+\left(\left(-\dfrac{260}{9}\right)\sqrt{7}\right)-\left(\left(\dfrac{375}{7}\right)\sqrt{7}\right)\right)+\left(-\dfrac{224}{9}\right)\\
&=&\left(27\right)\sqrt{7}+\dfrac{73}{3}+\left(-\dfrac{32}{3}\right)\sqrt{7}+\left(-\dfrac{295}{8}\right)\sqrt{7}+\dfrac{238}{3}+56-\left(\left(-\dfrac{19}{2}\right)\sqrt{7}\right)-56+\left(\left(-\dfrac{260}{9}\right)\sqrt{7}\right)-\left(\left(\dfrac{375}{7}\right)\sqrt{7}\right)-\dfrac{224}{9}\\
&=&\left(-\dfrac{47125}{504}\right)\sqrt{7}+\dfrac{709}{9}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(9\right)\sqrt{63}+\dfrac{73}{3}+\left(-\dfrac{16}{3}\right)\sqrt{28}+\left(-\dfrac{59}{8}\right)\sqrt{175}+\left(\dfrac{34}{3}\right)\sqrt{49}+\left(\left(8\right)\sqrt{49}\right)-\left(\left(-\dfrac{19}{4}\right)\sqrt{28}\right)-\left(\left(8\right)\sqrt{49}\right)+\left(\left(-\dfrac{52}{9}\right)\sqrt{175}\right)-\left(\left(\dfrac{75}{7}\right)\sqrt{175}\right)\right)-\left(\left(-\dfrac{32}{9}\right)\sqrt{49}\right)\\
&=&\left(\left(27\right)\sqrt{7}+\dfrac{73}{3}+\left(-\dfrac{32}{3}\right)\sqrt{7}+\left(-\dfrac{295}{8}\right)\sqrt{7}+\dfrac{238}{3}+56-\left(\left(-\dfrac{19}{2}\right)\sqrt{7}\right)-56+\left(\left(-\dfrac{260}{9}\right)\sqrt{7}\right)-\left(\left(\dfrac{375}{7}\right)\sqrt{7}\right)\right)-\left(-\dfrac{224}{9}\right)\\
&=&\left(\left(-\dfrac{47125}{504}\right)\sqrt{7}+\dfrac{311}{3}\right)-\left(-\dfrac{224}{9}\right)\\
&=&\left(-\dfrac{47125}{504}\right)\sqrt{7}+\dfrac{311}{3}+\dfrac{224}{9}\\
&=&\left(-\dfrac{47125}{504}\right)\sqrt{7}+\dfrac{1157}{9}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(9\right)\sqrt{63}+\dfrac{73}{3}+\left(-\dfrac{16}{3}\right)\sqrt{28}+\left(-\dfrac{59}{8}\right)\sqrt{175}+\left(\dfrac{34}{3}\right)\sqrt{49}+\left(\left(8\right)\sqrt{49}\right)-\left(\left(-\dfrac{19}{4}\right)\sqrt{28}\right)-\left(\left(8\right)\sqrt{49}\right)+\left(\left(-\dfrac{52}{9}\right)\sqrt{175}\right)-\left(\left(\dfrac{75}{7}\right)\sqrt{175}\right)\right)\times\left(\left(-\dfrac{32}{9}\right)\sqrt{49}\right)\\
&=&\left(\left(27\right)\sqrt{7}+\dfrac{73}{3}+\left(-\dfrac{32}{3}\right)\sqrt{7}+\left(-\dfrac{295}{8}\right)\sqrt{7}+\dfrac{238}{3}+56-\left(\left(-\dfrac{19}{2}\right)\sqrt{7}\right)-56+\left(\left(-\dfrac{260}{9}\right)\sqrt{7}\right)-\left(\left(\dfrac{375}{7}\right)\sqrt{7}\right)\right)\times\left(-\dfrac{224}{9}\right)\\
&=&\left(\left(-\dfrac{47125}{504}\right)\sqrt{7}+\dfrac{311}{3}\right)\left(-\dfrac{224}{9}\right)\\
&=&\left(\dfrac{188500}{81}\right)\sqrt{7}-\dfrac{69664}{27}\\
&=&\left(\dfrac{188500}{81}\right)\sqrt{7}-\dfrac{69664}{27}\\
\end{eqnarray*}