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 \[\left(0-\left(-4\right)\times1\right)\times\left(-4\right)+\left(\dfrac{9}{5}+\dfrac{8}{3}\right)\times\left(-\dfrac{8}{3}-0\right)\times\dfrac{9}{5}\times\left(1-\dfrac{8}{3}\right)\times0\times\left(-\dfrac{11}{2}-5\right)\times\dfrac{9}{5}-\dfrac{8}{3}\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\left(0-\left(-4\right)\times1\right)\times\left(-4\right)+\left(\dfrac{9}{5}+\dfrac{8}{3}\right)\times\left(-\dfrac{8}{3}-0\right)\times\dfrac{9}{5}\times\left(1-\dfrac{8}{3}\right)\times0\times\left(-\dfrac{11}{2}-5\right)\times\dfrac{9}{5}-\dfrac{8}{3}=-\dfrac{56}{3}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(0+4\right)\times\left(-4\right)+\left(\dfrac{9}{5}+\dfrac{8}{3}\right)\times\left(-\dfrac{8}{3}-0\right)\times\dfrac{9}{5}\times\left(1-\dfrac{8}{3}\right)\times0\times\left(-\dfrac{11}{2}-5\right)\times\dfrac{9}{5}-\dfrac{8}{3}\\&=&\left(0+4\right)\times\left(-4\right)+\left(\dfrac{9}{5}+\dfrac{8}{3}\right)\times-\dfrac{8}{3}\times\dfrac{9}{5}\times\left(1-\dfrac{8}{3}\right)\times0\times\left(-\dfrac{11}{2}-5\right)\times\dfrac{9}{5}-\dfrac{8}{3}\\&=&\left(0+4\right)\times\left(-4\right)+\left(\dfrac{9}{5}+\dfrac{8}{3}\right)\times-\dfrac{8}{3}\times\dfrac{9}{5}\times-\dfrac{5}{3}\times0\times\left(-\dfrac{11}{2}-5\right)\times\dfrac{9}{5}-\dfrac{8}{3}\\&=&\left(0+4\right)\times\left(-4\right)+\left(\dfrac{9}{5}+\dfrac{8}{3}\right)\times-\dfrac{8}{3}\times\dfrac{9}{5}\times-\dfrac{5}{3}\times0\times-\dfrac{21}{2}\times\dfrac{9}{5}-\dfrac{8}{3}\\&=&4\times\left(-4\right)+\left(\dfrac{9}{5}+\dfrac{8}{3}\right)\times-\dfrac{8}{3}\times\dfrac{9}{5}\times-\dfrac{5}{3}\times0\times-\dfrac{21}{2}\times\dfrac{9}{5}-\dfrac{8}{3}\\&=&4\times\left(-4\right)+\dfrac{67}{15}\times-\dfrac{8}{3}\times\dfrac{9}{5}\times-\dfrac{5}{3}\times0\times-\dfrac{21}{2}\times\dfrac{9}{5}-\dfrac{8}{3}\\&=&4\times\left(-4\right)+\dfrac{67}{15}\times\left(-\dfrac{24}{5}\right)\times-\dfrac{5}{3}\times0\times-\dfrac{21}{2}\times\dfrac{9}{5}-\dfrac{8}{3}\\&=&4\times\left(-4\right)+\dfrac{67}{15}\times8\times0\times-\dfrac{21}{2}\times\dfrac{9}{5}-\dfrac{8}{3}\\&=&4\times\left(-4\right)+\dfrac{67}{15}\times8\times0\times\dfrac{9}{5}-\dfrac{8}{3}\\&=&4\times\left(-4\right)+\dfrac{67}{15}\times8\times0-\dfrac{8}{3}\\&=&-16+\dfrac{67}{15}\times8\times0-\dfrac{8}{3}\\&=&-16+\dfrac{536}{15}\times0-\dfrac{8}{3}\\&=&-16+0-\dfrac{8}{3}\\&=&-16-\dfrac{8}{3}\\&=&-\dfrac{56}{3}\\
\end{eqnarray*}