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 \( X=0-\left(\left(\left(\dfrac{62}{3}\right)\sqrt{63}\right)-\left(\left(\dfrac{20}{3}\right)\sqrt{63}\right)-\left(\left(\dfrac{17}{9}\right)\sqrt{175}\right)+\dfrac{1}{9}+\dfrac{23}{5}\right)\) et \( Y=\left(\dfrac{1}{4}\right)\sqrt{49}+\dfrac{68}{5}+\dfrac{55}{3}+\left(\dfrac{4}{9}\right)\sqrt{175}+\left(7\right)\sqrt{63}\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(0-\left(\left(\left(\dfrac{62}{3}\right)\sqrt{63}\right)-\left(\left(\dfrac{20}{3}\right)\sqrt{63}\right)-\left(\left(\dfrac{17}{9}\right)\sqrt{175}\right)+\dfrac{1}{9}+\dfrac{23}{5}\right)\right)+\left(\left(\dfrac{1}{4}\right)\sqrt{49}+\dfrac{68}{5}+\dfrac{55}{3}+\left(\dfrac{4}{9}\right)\sqrt{175}+\left(7\right)\sqrt{63}\right)\\
&=&\left(0-\left(\left(\left(62\right)\sqrt{7}\right)-\left(\left(20\right)\sqrt{7}\right)-\left(\left(\dfrac{85}{9}\right)\sqrt{7}\right)+\dfrac{1}{9}+\dfrac{23}{5}\right)\right)+\left(\dfrac{7}{4}+\dfrac{68}{5}+\dfrac{55}{3}+\left(\dfrac{20}{9}\right)\sqrt{7}+\left(21\right)\sqrt{7}\right)\\
&=&0-\left(\left(\left(62\right)\sqrt{7}\right)-\left(\left(20\right)\sqrt{7}\right)-\left(\left(\dfrac{85}{9}\right)\sqrt{7}\right)+\dfrac{1}{9}+\dfrac{23}{5}\right)+\dfrac{7}{4}+\dfrac{68}{5}+\dfrac{55}{3}+\left(\dfrac{20}{9}\right)\sqrt{7}+\left(21\right)\sqrt{7}\\
&=&\dfrac{1043}{36}+\left(-\dfrac{28}{3}\right)\sqrt{7}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(0-\left(\left(\left(\dfrac{62}{3}\right)\sqrt{63}\right)-\left(\left(\dfrac{20}{3}\right)\sqrt{63}\right)-\left(\left(\dfrac{17}{9}\right)\sqrt{175}\right)+\dfrac{1}{9}+\dfrac{23}{5}\right)\right)-\left(\left(\dfrac{1}{4}\right)\sqrt{49}+\dfrac{68}{5}+\dfrac{55}{3}+\left(\dfrac{4}{9}\right)\sqrt{175}+\left(7\right)\sqrt{63}\right)\\
&=&\left(0-\left(\left(\left(62\right)\sqrt{7}\right)-\left(\left(20\right)\sqrt{7}\right)-\left(\left(\dfrac{85}{9}\right)\sqrt{7}\right)+\dfrac{1}{9}+\dfrac{23}{5}\right)\right)-\left(\dfrac{7}{4}+\dfrac{68}{5}+\dfrac{55}{3}+\left(\dfrac{20}{9}\right)\sqrt{7}+\left(21\right)\sqrt{7}\right)\\
&=&\left(-\dfrac{212}{45}+\left(-\dfrac{293}{9}\right)\sqrt{7}\right)-\left(\dfrac{2021}{60}+\left(\dfrac{209}{9}\right)\sqrt{7}\right)\\
&=&-\dfrac{212}{45}+\left(-\dfrac{293}{9}\right)\sqrt{7}+-\dfrac{2021}{60}+\left(-\dfrac{209}{9}\right)\sqrt{7}\\
&=&-\dfrac{6911}{180}+\left(-\dfrac{502}{9}\right)\sqrt{7}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(0-\left(\left(\left(\dfrac{62}{3}\right)\sqrt{63}\right)-\left(\left(\dfrac{20}{3}\right)\sqrt{63}\right)-\left(\left(\dfrac{17}{9}\right)\sqrt{175}\right)+\dfrac{1}{9}+\dfrac{23}{5}\right)\right)\times\left(\left(\dfrac{1}{4}\right)\sqrt{49}+\dfrac{68}{5}+\dfrac{55}{3}+\left(\dfrac{4}{9}\right)\sqrt{175}+\left(7\right)\sqrt{63}\right)\\
&=&\left(0-\left(\left(\left(62\right)\sqrt{7}\right)-\left(\left(20\right)\sqrt{7}\right)-\left(\left(\dfrac{85}{9}\right)\sqrt{7}\right)+\dfrac{1}{9}+\dfrac{23}{5}\right)\right)\times\left(\dfrac{7}{4}+\dfrac{68}{5}+\dfrac{55}{3}+\left(\dfrac{20}{9}\right)\sqrt{7}+\left(21\right)\sqrt{7}\right)\\
&=&\left(-\dfrac{212}{45}+\left(-\dfrac{293}{9}\right)\sqrt{7}\right)\left(\dfrac{2021}{60}+\left(\dfrac{209}{9}\right)\sqrt{7}\right)\\
&=&-\dfrac{107113}{675}+\left(-\dfrac{1953691}{1620}\right)\sqrt{7}+\left(-\dfrac{61237}{81}\right)\sqrt{49}\\
&=&-\dfrac{11037814}{2025}+\left(-\dfrac{1953691}{1620}\right)\sqrt{7}\\
\end{eqnarray*}