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 \( X=\left(\left(\dfrac{11}{2}\right)\sqrt{28}\right)-\left(\left(\left(\dfrac{2}{7}\right)\sqrt{28}\right)+\dfrac{59}{9}+\dfrac{33}{4}\right)-\left(\left(-\dfrac{3}{2}\right)\sqrt{49}\right)-\left(\left(-\dfrac{68}{7}\right)\sqrt{49}\right)\) et \( Y=\left(\dfrac{13}{3}\right)\sqrt{28}+\left(-\dfrac{15}{2}\right)\sqrt{63}+\left(-\dfrac{13}{4}\right)\sqrt{175}+\left(3\right)\sqrt{63}+\left(-\dfrac{13}{4}\right)\sqrt{175}+\dfrac{53}{3}+1+\left(-\dfrac{2}{5}\right)\sqrt{28}\) . 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(\dfrac{11}{2}\right)\sqrt{28}\right)-\left(\left(\left(\dfrac{2}{7}\right)\sqrt{28}\right)+\dfrac{59}{9}+\dfrac{33}{4}\right)-\left(\left(-\dfrac{3}{2}\right)\sqrt{49}\right)-\left(\left(-\dfrac{68}{7}\right)\sqrt{49}\right)\right)+\left(\left(\dfrac{13}{3}\right)\sqrt{28}+\left(-\dfrac{15}{2}\right)\sqrt{63}+\left(-\dfrac{13}{4}\right)\sqrt{175}+\left(3\right)\sqrt{63}+\left(-\dfrac{13}{4}\right)\sqrt{175}+\dfrac{53}{3}+1+\left(-\dfrac{2}{5}\right)\sqrt{28}\right)\\
&=&\left(\left(\left(11\right)\sqrt{7}\right)-\left(\left(\left(\dfrac{4}{7}\right)\sqrt{7}\right)+\dfrac{59}{9}+\dfrac{33}{4}\right)+\dfrac{21}{2}+68\right)+\left(\left(\dfrac{26}{3}\right)\sqrt{7}+\left(-\dfrac{45}{2}\right)\sqrt{7}+\left(-\dfrac{65}{4}\right)\sqrt{7}+\left(9\right)\sqrt{7}+\left(-\dfrac{65}{4}\right)\sqrt{7}+\dfrac{53}{3}+1+\left(-\dfrac{4}{5}\right)\sqrt{7}\right)\\
&=&\left(\left(11\right)\sqrt{7}\right)-\left(\left(\left(\dfrac{4}{7}\right)\sqrt{7}\right)+\dfrac{59}{9}+\dfrac{33}{4}\right)+\dfrac{21}{2}+68+\left(\dfrac{26}{3}\right)\sqrt{7}+\left(-\dfrac{45}{2}\right)\sqrt{7}+\left(-\dfrac{65}{4}\right)\sqrt{7}+\left(9\right)\sqrt{7}+\left(-\dfrac{65}{4}\right)\sqrt{7}+\dfrac{53}{3}+1+\left(-\dfrac{4}{5}\right)\sqrt{7}\\
&=&\left(-\dfrac{2909}{105}\right)\sqrt{7}+\dfrac{2965}{36}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\left(\dfrac{11}{2}\right)\sqrt{28}\right)-\left(\left(\left(\dfrac{2}{7}\right)\sqrt{28}\right)+\dfrac{59}{9}+\dfrac{33}{4}\right)-\left(\left(-\dfrac{3}{2}\right)\sqrt{49}\right)-\left(\left(-\dfrac{68}{7}\right)\sqrt{49}\right)\right)-\left(\left(\dfrac{13}{3}\right)\sqrt{28}+\left(-\dfrac{15}{2}\right)\sqrt{63}+\left(-\dfrac{13}{4}\right)\sqrt{175}+\left(3\right)\sqrt{63}+\left(-\dfrac{13}{4}\right)\sqrt{175}+\dfrac{53}{3}+1+\left(-\dfrac{2}{5}\right)\sqrt{28}\right)\\
&=&\left(\left(\left(11\right)\sqrt{7}\right)-\left(\left(\left(\dfrac{4}{7}\right)\sqrt{7}\right)+\dfrac{59}{9}+\dfrac{33}{4}\right)+\dfrac{21}{2}+68\right)-\left(\left(\dfrac{26}{3}\right)\sqrt{7}+\left(-\dfrac{45}{2}\right)\sqrt{7}+\left(-\dfrac{65}{4}\right)\sqrt{7}+\left(9\right)\sqrt{7}+\left(-\dfrac{65}{4}\right)\sqrt{7}+\dfrac{53}{3}+1+\left(-\dfrac{4}{5}\right)\sqrt{7}\right)\\
&=&\left(\left(\dfrac{73}{7}\right)\sqrt{7}+\dfrac{2293}{36}\right)-\left(\left(-\dfrac{572}{15}\right)\sqrt{7}+\dfrac{56}{3}\right)\\
&=&\left(\dfrac{73}{7}\right)\sqrt{7}+\dfrac{2293}{36}+\left(\dfrac{572}{15}\right)\sqrt{7}-\dfrac{56}{3}\\
&=&\left(\dfrac{5099}{105}\right)\sqrt{7}+\dfrac{1621}{36}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\left(\dfrac{11}{2}\right)\sqrt{28}\right)-\left(\left(\left(\dfrac{2}{7}\right)\sqrt{28}\right)+\dfrac{59}{9}+\dfrac{33}{4}\right)-\left(\left(-\dfrac{3}{2}\right)\sqrt{49}\right)-\left(\left(-\dfrac{68}{7}\right)\sqrt{49}\right)\right)\times\left(\left(\dfrac{13}{3}\right)\sqrt{28}+\left(-\dfrac{15}{2}\right)\sqrt{63}+\left(-\dfrac{13}{4}\right)\sqrt{175}+\left(3\right)\sqrt{63}+\left(-\dfrac{13}{4}\right)\sqrt{175}+\dfrac{53}{3}+1+\left(-\dfrac{2}{5}\right)\sqrt{28}\right)\\
&=&\left(\left(\left(11\right)\sqrt{7}\right)-\left(\left(\left(\dfrac{4}{7}\right)\sqrt{7}\right)+\dfrac{59}{9}+\dfrac{33}{4}\right)+\dfrac{21}{2}+68\right)\times\left(\left(\dfrac{26}{3}\right)\sqrt{7}+\left(-\dfrac{45}{2}\right)\sqrt{7}+\left(-\dfrac{65}{4}\right)\sqrt{7}+\left(9\right)\sqrt{7}+\left(-\dfrac{65}{4}\right)\sqrt{7}+\dfrac{53}{3}+1+\left(-\dfrac{4}{5}\right)\sqrt{7}\right)\\
&=&\left(\left(\dfrac{73}{7}\right)\sqrt{7}+\dfrac{2293}{36}\right)\left(\left(-\dfrac{572}{15}\right)\sqrt{7}+\dfrac{56}{3}\right)\\
&=&\left(-\dfrac{41756}{105}\right)\sqrt{49}+\left(-\dfrac{301619}{135}\right)\sqrt{7}+\dfrac{32102}{27}\\
&=&-\dfrac{215294}{135}+\left(-\dfrac{301619}{135}\right)\sqrt{7}\\
\end{eqnarray*}