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
Calculer \[\left(4-2+\dfrac{31}{2}+3+\dfrac{19}{6}\right)\times\dfrac{19}{6}\times4+\left(0+2-5+0+4-4+2\right)-\left(-\dfrac{14}{5}-\dfrac{31}{2}-\dfrac{19}{6}\right)+5\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\left(4-2+\dfrac{31}{2}+3+\dfrac{19}{6}\right)\times\dfrac{19}{6}\times4+\left(0+2-5+0+4-4+2\right)-\left(-\dfrac{14}{5}-\dfrac{31}{2}-\dfrac{19}{6}\right)+5=\dfrac{14636}{45}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(4+\dfrac{27}{2}+3+\dfrac{19}{6}\right)\times\dfrac{19}{6}\times4+\left(0+2-5+0+4-4+2\right)-\left(-\dfrac{14}{5}-\dfrac{31}{2}-\dfrac{19}{6}\right)+5\\&=&\left(4+\dfrac{27}{2}+\dfrac{37}{6}\right)\times\dfrac{19}{6}\times4+\left(0+2-5+0+4-4+2\right)-\left(-\dfrac{14}{5}-\dfrac{31}{2}-\dfrac{19}{6}\right)+5\\&=&\left(4+\dfrac{27}{2}+\dfrac{37}{6}\right)\times\dfrac{19}{6}\times4+\left(2-5+0+4-4+2\right)-\left(-\dfrac{14}{5}-\dfrac{31}{2}-\dfrac{19}{6}\right)+5\\&=&\left(4+\dfrac{27}{2}+\dfrac{37}{6}\right)\times\dfrac{19}{6}\times4+\left(-3+0+4-4+2\right)-\left(-\dfrac{14}{5}-\dfrac{31}{2}-\dfrac{19}{6}\right)+5\\&=&\left(4+\dfrac{27}{2}+\dfrac{37}{6}\right)\times\dfrac{19}{6}\times4+\left(-3+0+0+2\right)-\left(-\dfrac{14}{5}-\dfrac{31}{2}-\dfrac{19}{6}\right)+5\\&=&\left(4+\dfrac{27}{2}+\dfrac{37}{6}\right)\times\dfrac{19}{6}\times4+\left(-3+0+2\right)-\left(-\dfrac{14}{5}-\dfrac{31}{2}-\dfrac{19}{6}\right)+5\\&=&\left(\dfrac{35}{2}+\dfrac{37}{6}\right)\times\dfrac{19}{6}\times4+\left(-3+0+2\right)-\left(-\dfrac{14}{5}-\dfrac{31}{2}-\dfrac{19}{6}\right)+5\\&=&\dfrac{71}{3}\times\dfrac{19}{6}\times4+\left(-3+0+2\right)-\left(-\dfrac{14}{5}-\dfrac{31}{2}-\dfrac{19}{6}\right)+5\\&=&\dfrac{71}{3}\times\dfrac{19}{6}\times4+\left(-3+2\right)-\left(-\dfrac{14}{5}-\dfrac{31}{2}-\dfrac{19}{6}\right)+5\\&=&\dfrac{71}{3}\times\dfrac{19}{6}\times4-1-\left(-\dfrac{14}{5}-\dfrac{31}{2}-\dfrac{19}{6}\right)+5\\&=&\dfrac{71}{3}\times\dfrac{19}{6}\times4-1-\left(-\dfrac{183}{10}-\dfrac{19}{6}\right)+5\\&=&\dfrac{71}{3}\times\dfrac{19}{6}\times4-1+\dfrac{322}{15}+5\\&=&\dfrac{1349}{18}\times4-1+\dfrac{322}{15}+5\\&=&\dfrac{2698}{9}-1+\dfrac{322}{15}+5\\&=&\dfrac{2698}{9}+\dfrac{307}{15}+5\\&=&\dfrac{14411}{45}+5\\&=&\dfrac{14636}{45}\\
\end{eqnarray*}