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 \( X=\left(\left(-6\right)\sqrt{25}\right)-\dfrac{5}{2}-\left(\left(-\dfrac{47}{8}\right)\sqrt{20}+\left(\dfrac{25}{9}\right)\sqrt{25}\right)\) et \( Y=\left(\left(\dfrac{63}{8}\right)\sqrt{25}\right)-\left(\left(1\right)\sqrt{45}+\left(2\right)\sqrt{25}+\left(\dfrac{75}{2}\right)\sqrt{25}\right)\) . 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(-6\right)\sqrt{25}\right)-\dfrac{5}{2}-\left(\left(-\dfrac{47}{8}\right)\sqrt{20}+\left(\dfrac{25}{9}\right)\sqrt{25}\right)\right)+\left(\left(\left(\dfrac{63}{8}\right)\sqrt{25}\right)-\left(\left(1\right)\sqrt{45}+\left(2\right)\sqrt{25}+\left(\dfrac{75}{2}\right)\sqrt{25}\right)\right)\\
&=&\left(-30-\dfrac{5}{2}-\left(\left(-\dfrac{47}{4}\right)\sqrt{5}+\dfrac{125}{9}\right)\right)+\left(\dfrac{315}{8}-\left(\left(3\right)\sqrt{5}+10+\dfrac{375}{2}\right)\right)\\
&=&-30-\dfrac{5}{2}-\left(\left(-\dfrac{47}{4}\right)\sqrt{5}+\dfrac{125}{9}\right)+\dfrac{315}{8}-\left(\left(3\right)\sqrt{5}+10+\dfrac{375}{2}\right)\\
&=&-\dfrac{14725}{72}+\left(\dfrac{35}{4}\right)\sqrt{5}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\left(-6\right)\sqrt{25}\right)-\dfrac{5}{2}-\left(\left(-\dfrac{47}{8}\right)\sqrt{20}+\left(\dfrac{25}{9}\right)\sqrt{25}\right)\right)-\left(\left(\left(\dfrac{63}{8}\right)\sqrt{25}\right)-\left(\left(1\right)\sqrt{45}+\left(2\right)\sqrt{25}+\left(\dfrac{75}{2}\right)\sqrt{25}\right)\right)\\
&=&\left(-30-\dfrac{5}{2}-\left(\left(-\dfrac{47}{4}\right)\sqrt{5}+\dfrac{125}{9}\right)\right)-\left(\dfrac{315}{8}-\left(\left(3\right)\sqrt{5}+10+\dfrac{375}{2}\right)\right)\\
&=&\left(-\dfrac{835}{18}+\left(\dfrac{47}{4}\right)\sqrt{5}\right)-\left(-\dfrac{1265}{8}+\left(-3\right)\sqrt{5}\right)\\
&=&-\dfrac{835}{18}+\left(\dfrac{47}{4}\right)\sqrt{5}+\dfrac{1265}{8}+\left(3\right)\sqrt{5}\\
&=&\dfrac{8045}{72}+\left(\dfrac{59}{4}\right)\sqrt{5}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\left(-6\right)\sqrt{25}\right)-\dfrac{5}{2}-\left(\left(-\dfrac{47}{8}\right)\sqrt{20}+\left(\dfrac{25}{9}\right)\sqrt{25}\right)\right)\times\left(\left(\left(\dfrac{63}{8}\right)\sqrt{25}\right)-\left(\left(1\right)\sqrt{45}+\left(2\right)\sqrt{25}+\left(\dfrac{75}{2}\right)\sqrt{25}\right)\right)\\
&=&\left(-30-\dfrac{5}{2}-\left(\left(-\dfrac{47}{4}\right)\sqrt{5}+\dfrac{125}{9}\right)\right)\times\left(\dfrac{315}{8}-\left(\left(3\right)\sqrt{5}+10+\dfrac{375}{2}\right)\right)\\
&=&\left(-\dfrac{835}{18}+\left(\dfrac{47}{4}\right)\sqrt{5}\right)\left(-\dfrac{1265}{8}+\left(-3\right)\sqrt{5}\right)\\
&=&\dfrac{1056275}{144}+\left(-\dfrac{165005}{96}\right)\sqrt{5}+\left(-\dfrac{141}{4}\right)\sqrt{25}\\
&=&\dfrac{1030895}{144}+\left(-\dfrac{165005}{96}\right)\sqrt{5}\\
\end{eqnarray*}