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 \( X=\left(\left(\left(\dfrac{13}{2}\right)\sqrt{20}\right)-\left(\left(1\right)\sqrt{20}\right)+3\right)-\left(\left(\dfrac{72}{7}\right)\sqrt{20}+\left(\dfrac{57}{5}\right)\sqrt{20}\right)+\dfrac{14}{3}\) et \( Y=\left(\left(\dfrac{21}{2}\right)\sqrt{20}+\left(4\right)\sqrt{25}\right)-\left(\left(-\dfrac{73}{2}\right)\sqrt{25}\right)\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(\left(\left(\left(\dfrac{13}{2}\right)\sqrt{20}\right)-\left(\left(1\right)\sqrt{20}\right)+3\right)-\left(\left(\dfrac{72}{7}\right)\sqrt{20}+\left(\dfrac{57}{5}\right)\sqrt{20}\right)+\dfrac{14}{3}\right)+\left(\left(\left(\dfrac{21}{2}\right)\sqrt{20}+\left(4\right)\sqrt{25}\right)-\left(\left(-\dfrac{73}{2}\right)\sqrt{25}\right)\right)\\
&=&\left(\left(\left(\left(13\right)\sqrt{5}\right)-\left(\left(2\right)\sqrt{5}\right)+3\right)-\left(\left(\dfrac{144}{7}\right)\sqrt{5}+\left(\dfrac{114}{5}\right)\sqrt{5}\right)+\dfrac{14}{3}\right)+\left(\left(\left(21\right)\sqrt{5}+20\right)+\dfrac{365}{2}\right)\\
&=&\left(\left(\left(13\right)\sqrt{5}\right)-\left(\left(2\right)\sqrt{5}\right)+3\right)-\left(\left(\dfrac{144}{7}\right)\sqrt{5}+\left(\dfrac{114}{5}\right)\sqrt{5}\right)+\dfrac{14}{3}+\left(\left(21\right)\sqrt{5}+20\right)+\dfrac{365}{2}\\
&=&\left(-\dfrac{398}{35}\right)\sqrt{5}+\dfrac{1261}{6}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\left(\left(\dfrac{13}{2}\right)\sqrt{20}\right)-\left(\left(1\right)\sqrt{20}\right)+3\right)-\left(\left(\dfrac{72}{7}\right)\sqrt{20}+\left(\dfrac{57}{5}\right)\sqrt{20}\right)+\dfrac{14}{3}\right)-\left(\left(\left(\dfrac{21}{2}\right)\sqrt{20}+\left(4\right)\sqrt{25}\right)-\left(\left(-\dfrac{73}{2}\right)\sqrt{25}\right)\right)\\
&=&\left(\left(\left(\left(13\right)\sqrt{5}\right)-\left(\left(2\right)\sqrt{5}\right)+3\right)-\left(\left(\dfrac{144}{7}\right)\sqrt{5}+\left(\dfrac{114}{5}\right)\sqrt{5}\right)+\dfrac{14}{3}\right)-\left(\left(\left(21\right)\sqrt{5}+20\right)+\dfrac{365}{2}\right)\\
&=&\left(\left(-\dfrac{1133}{35}\right)\sqrt{5}+\dfrac{23}{3}\right)-\left(\left(21\right)\sqrt{5}+\dfrac{405}{2}\right)\\
&=&\left(-\dfrac{1133}{35}\right)\sqrt{5}+\dfrac{23}{3}+\left(-21\right)\sqrt{5}-\dfrac{405}{2}\\
&=&\left(-\dfrac{1868}{35}\right)\sqrt{5}-\dfrac{1169}{6}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\left(\left(\dfrac{13}{2}\right)\sqrt{20}\right)-\left(\left(1\right)\sqrt{20}\right)+3\right)-\left(\left(\dfrac{72}{7}\right)\sqrt{20}+\left(\dfrac{57}{5}\right)\sqrt{20}\right)+\dfrac{14}{3}\right)\times\left(\left(\left(\dfrac{21}{2}\right)\sqrt{20}+\left(4\right)\sqrt{25}\right)-\left(\left(-\dfrac{73}{2}\right)\sqrt{25}\right)\right)\\
&=&\left(\left(\left(\left(13\right)\sqrt{5}\right)-\left(\left(2\right)\sqrt{5}\right)+3\right)-\left(\left(\dfrac{144}{7}\right)\sqrt{5}+\left(\dfrac{114}{5}\right)\sqrt{5}\right)+\dfrac{14}{3}\right)\times\left(\left(\left(21\right)\sqrt{5}+20\right)+\dfrac{365}{2}\right)\\
&=&\left(\left(-\dfrac{1133}{35}\right)\sqrt{5}+\dfrac{23}{3}\right)\left(\left(21\right)\sqrt{5}+\dfrac{405}{2}\right)\\
&=&\left(-\dfrac{3399}{5}\right)\sqrt{25}+\left(-\dfrac{89519}{14}\right)\sqrt{5}+\dfrac{3105}{2}\\
&=&-\dfrac{3693}{2}+\left(-\dfrac{89519}{14}\right)\sqrt{5}\\
\end{eqnarray*}