L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
Si vous regénérez la page (F5) les valeurs seront changées.
La correction se trouve en bas de page.
Exercice
Soit \( X=\left(\left(\left(-\dfrac{66}{5}\right)\sqrt{4}\right)-\left(\left(\dfrac{61}{9}\right)\sqrt{8}\right)-\left(\left(-\dfrac{47}{8}\right)\sqrt{8}\right)\right)-\left(\left(-6\right)\sqrt{50}\right)-\left(-\dfrac{37}{8}+\left(-\dfrac{47}{8}\right)\sqrt{8}+\left(4\right)\sqrt{4}-\dfrac{9}{7}\right)\) et \( Y=\left(\left(-\dfrac{7}{4}\right)\sqrt{18}\right)-\left(\left(-\dfrac{52}{9}\right)\sqrt{18}\right)-0+\left(-\dfrac{7}{4}\right)\sqrt{18}\) . 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(\left(-\dfrac{66}{5}\right)\sqrt{4}\right)-\left(\left(\dfrac{61}{9}\right)\sqrt{8}\right)-\left(\left(-\dfrac{47}{8}\right)\sqrt{8}\right)\right)-\left(\left(-6\right)\sqrt{50}\right)-\left(-\dfrac{37}{8}+\left(-\dfrac{47}{8}\right)\sqrt{8}+\left(4\right)\sqrt{4}-\dfrac{9}{7}\right)\right)+\left(\left(\left(-\dfrac{7}{4}\right)\sqrt{18}\right)-\left(\left(-\dfrac{52}{9}\right)\sqrt{18}\right)-0+\left(-\dfrac{7}{4}\right)\sqrt{18}\right)\\
&=&\left(\left(-\dfrac{132}{5}-\left(\left(\dfrac{122}{9}\right)\sqrt{2}\right)-\left(\left(-\dfrac{47}{4}\right)\sqrt{2}\right)\right)-\left(\left(-30\right)\sqrt{2}\right)-\left(-\dfrac{37}{8}+\left(-\dfrac{47}{4}\right)\sqrt{2}+8-\dfrac{9}{7}\right)\right)+\left(\left(\left(-\dfrac{21}{4}\right)\sqrt{2}\right)-\left(\left(-\dfrac{52}{3}\right)\sqrt{2}\right)-0+\left(-\dfrac{21}{4}\right)\sqrt{2}\right)\\
&=&\left(-\dfrac{132}{5}-\left(\left(\dfrac{122}{9}\right)\sqrt{2}\right)-\left(\left(-\dfrac{47}{4}\right)\sqrt{2}\right)\right)-\left(\left(-30\right)\sqrt{2}\right)-\left(-\dfrac{37}{8}+\left(-\dfrac{47}{4}\right)\sqrt{2}+8-\dfrac{9}{7}\right)+\left(\left(-\dfrac{21}{4}\right)\sqrt{2}\right)-\left(\left(-\dfrac{52}{3}\right)\sqrt{2}\right)-0+\left(-\dfrac{21}{4}\right)\sqrt{2}\\
&=&-\dfrac{7977}{280}+\left(\dfrac{421}{9}\right)\sqrt{2}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\left(\left(-\dfrac{66}{5}\right)\sqrt{4}\right)-\left(\left(\dfrac{61}{9}\right)\sqrt{8}\right)-\left(\left(-\dfrac{47}{8}\right)\sqrt{8}\right)\right)-\left(\left(-6\right)\sqrt{50}\right)-\left(-\dfrac{37}{8}+\left(-\dfrac{47}{8}\right)\sqrt{8}+\left(4\right)\sqrt{4}-\dfrac{9}{7}\right)\right)-\left(\left(\left(-\dfrac{7}{4}\right)\sqrt{18}\right)-\left(\left(-\dfrac{52}{9}\right)\sqrt{18}\right)-0+\left(-\dfrac{7}{4}\right)\sqrt{18}\right)\\
&=&\left(\left(-\dfrac{132}{5}-\left(\left(\dfrac{122}{9}\right)\sqrt{2}\right)-\left(\left(-\dfrac{47}{4}\right)\sqrt{2}\right)\right)-\left(\left(-30\right)\sqrt{2}\right)-\left(-\dfrac{37}{8}+\left(-\dfrac{47}{4}\right)\sqrt{2}+8-\dfrac{9}{7}\right)\right)-\left(\left(\left(-\dfrac{21}{4}\right)\sqrt{2}\right)-\left(\left(-\dfrac{52}{3}\right)\sqrt{2}\right)-0+\left(-\dfrac{21}{4}\right)\sqrt{2}\right)\\
&=&\left(-\dfrac{7977}{280}+\left(\dfrac{719}{18}\right)\sqrt{2}\right)-\left(\left(\dfrac{41}{6}\right)\sqrt{2}+0\right)\\
&=&-\dfrac{7977}{280}+\left(\dfrac{719}{18}\right)\sqrt{2}+\left(-\dfrac{41}{6}\right)\sqrt{2}+0\\
&=&-\dfrac{7977}{280}+\left(\dfrac{298}{9}\right)\sqrt{2}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\left(\left(-\dfrac{66}{5}\right)\sqrt{4}\right)-\left(\left(\dfrac{61}{9}\right)\sqrt{8}\right)-\left(\left(-\dfrac{47}{8}\right)\sqrt{8}\right)\right)-\left(\left(-6\right)\sqrt{50}\right)-\left(-\dfrac{37}{8}+\left(-\dfrac{47}{8}\right)\sqrt{8}+\left(4\right)\sqrt{4}-\dfrac{9}{7}\right)\right)\times\left(\left(\left(-\dfrac{7}{4}\right)\sqrt{18}\right)-\left(\left(-\dfrac{52}{9}\right)\sqrt{18}\right)-0+\left(-\dfrac{7}{4}\right)\sqrt{18}\right)\\
&=&\left(\left(-\dfrac{132}{5}-\left(\left(\dfrac{122}{9}\right)\sqrt{2}\right)-\left(\left(-\dfrac{47}{4}\right)\sqrt{2}\right)\right)-\left(\left(-30\right)\sqrt{2}\right)-\left(-\dfrac{37}{8}+\left(-\dfrac{47}{4}\right)\sqrt{2}+8-\dfrac{9}{7}\right)\right)\times\left(\left(\left(-\dfrac{21}{4}\right)\sqrt{2}\right)-\left(\left(-\dfrac{52}{3}\right)\sqrt{2}\right)-0+\left(-\dfrac{21}{4}\right)\sqrt{2}\right)\\
&=&\left(-\dfrac{7977}{280}+\left(\dfrac{719}{18}\right)\sqrt{2}\right)\left(\left(\dfrac{41}{6}\right)\sqrt{2}+0\right)\\
&=&\left(-\dfrac{109019}{560}\right)\sqrt{2}+0+\left(\dfrac{29479}{108}\right)\sqrt{4}\\
&=&\left(-\dfrac{109019}{560}\right)\sqrt{2}+\dfrac{29479}{54}\\
\end{eqnarray*}