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 \( X=\left(-\dfrac{35}{4}+\left(\dfrac{49}{8}\right)\sqrt{45}+\left(3\right)\sqrt{125}+\dfrac{54}{5}\right)+\dfrac{58}{7}-\dfrac{13}{2}-\left(\left(\left(-\dfrac{3}{4}\right)\sqrt{45}\right)-\left(\left(-\dfrac{3}{4}\right)\sqrt{45}\right)-\left(\left(\dfrac{52}{7}\right)\sqrt{45}\right)-\left(\left(-\dfrac{33}{8}\right)\sqrt{20}\right)\right)\) et \( Y=\left(-4\right)\sqrt{25}\) . 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{35}{4}+\left(\dfrac{49}{8}\right)\sqrt{45}+\left(3\right)\sqrt{125}+\dfrac{54}{5}\right)+\dfrac{58}{7}-\dfrac{13}{2}-\left(\left(\left(-\dfrac{3}{4}\right)\sqrt{45}\right)-\left(\left(-\dfrac{3}{4}\right)\sqrt{45}\right)-\left(\left(\dfrac{52}{7}\right)\sqrt{45}\right)-\left(\left(-\dfrac{33}{8}\right)\sqrt{20}\right)\right)\right)+\left(\left(-4\right)\sqrt{25}\right)\\
&=&\left(\left(-\dfrac{35}{4}+\left(\dfrac{147}{8}\right)\sqrt{5}+\left(15\right)\sqrt{5}+\dfrac{54}{5}\right)+\dfrac{58}{7}-\dfrac{13}{2}-\left(\left(\left(-\dfrac{9}{4}\right)\sqrt{5}\right)-\left(\left(-\dfrac{9}{4}\right)\sqrt{5}\right)-\left(\left(\dfrac{156}{7}\right)\sqrt{5}\right)-\left(\left(-\dfrac{33}{4}\right)\sqrt{5}\right)\right)\right)+\left(-20\right)\\
&=&\left(-\dfrac{35}{4}+\left(\dfrac{147}{8}\right)\sqrt{5}+\left(15\right)\sqrt{5}+\dfrac{54}{5}\right)+\dfrac{58}{7}-\dfrac{13}{2}-\left(\left(\left(-\dfrac{9}{4}\right)\sqrt{5}\right)-\left(\left(-\dfrac{9}{4}\right)\sqrt{5}\right)-\left(\left(\dfrac{156}{7}\right)\sqrt{5}\right)-\left(\left(-\dfrac{33}{4}\right)\sqrt{5}\right)\right)-20\\
&=&-\dfrac{2263}{140}+\left(\dfrac{2655}{56}\right)\sqrt{5}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(-\dfrac{35}{4}+\left(\dfrac{49}{8}\right)\sqrt{45}+\left(3\right)\sqrt{125}+\dfrac{54}{5}\right)+\dfrac{58}{7}-\dfrac{13}{2}-\left(\left(\left(-\dfrac{3}{4}\right)\sqrt{45}\right)-\left(\left(-\dfrac{3}{4}\right)\sqrt{45}\right)-\left(\left(\dfrac{52}{7}\right)\sqrt{45}\right)-\left(\left(-\dfrac{33}{8}\right)\sqrt{20}\right)\right)\right)-\left(\left(-4\right)\sqrt{25}\right)\\
&=&\left(\left(-\dfrac{35}{4}+\left(\dfrac{147}{8}\right)\sqrt{5}+\left(15\right)\sqrt{5}+\dfrac{54}{5}\right)+\dfrac{58}{7}-\dfrac{13}{2}-\left(\left(\left(-\dfrac{9}{4}\right)\sqrt{5}\right)-\left(\left(-\dfrac{9}{4}\right)\sqrt{5}\right)-\left(\left(\dfrac{156}{7}\right)\sqrt{5}\right)-\left(\left(-\dfrac{33}{4}\right)\sqrt{5}\right)\right)\right)-\left(-20\right)\\
&=&\left(\dfrac{537}{140}+\left(\dfrac{2655}{56}\right)\sqrt{5}\right)-\left(-20\right)\\
&=&\dfrac{537}{140}+\left(\dfrac{2655}{56}\right)\sqrt{5}+20\\
&=&\dfrac{3337}{140}+\left(\dfrac{2655}{56}\right)\sqrt{5}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(-\dfrac{35}{4}+\left(\dfrac{49}{8}\right)\sqrt{45}+\left(3\right)\sqrt{125}+\dfrac{54}{5}\right)+\dfrac{58}{7}-\dfrac{13}{2}-\left(\left(\left(-\dfrac{3}{4}\right)\sqrt{45}\right)-\left(\left(-\dfrac{3}{4}\right)\sqrt{45}\right)-\left(\left(\dfrac{52}{7}\right)\sqrt{45}\right)-\left(\left(-\dfrac{33}{8}\right)\sqrt{20}\right)\right)\right)\times\left(\left(-4\right)\sqrt{25}\right)\\
&=&\left(\left(-\dfrac{35}{4}+\left(\dfrac{147}{8}\right)\sqrt{5}+\left(15\right)\sqrt{5}+\dfrac{54}{5}\right)+\dfrac{58}{7}-\dfrac{13}{2}-\left(\left(\left(-\dfrac{9}{4}\right)\sqrt{5}\right)-\left(\left(-\dfrac{9}{4}\right)\sqrt{5}\right)-\left(\left(\dfrac{156}{7}\right)\sqrt{5}\right)-\left(\left(-\dfrac{33}{4}\right)\sqrt{5}\right)\right)\right)\times\left(-20\right)\\
&=&\left(\dfrac{537}{140}+\left(\dfrac{2655}{56}\right)\sqrt{5}\right)\left(-20\right)\\
&=&-\dfrac{537}{7}+\left(-\dfrac{13275}{14}\right)\sqrt{5}\\
&=&-\dfrac{537}{7}+\left(-\dfrac{13275}{14}\right)\sqrt{5}\\
\end{eqnarray*}