L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[\left(-\dfrac{49}{2}+\dfrac{129}{4}+\dfrac{\dfrac{\dfrac{-\dfrac{49}{2}}{\dfrac{61}{6}\times2\times\left(-6\right)\times\dfrac{129}{4}}}{3}}{-9}+\dfrac{3}{2}\times\left(-\dfrac{55}{6}\right)-\dfrac{63}{2}\right)\times\dfrac{\dfrac{\dfrac{-12}{-9}}{-\dfrac{16}{5}}}{-\dfrac{140}{11}}\times\left(-\dfrac{63}{2}\right)\times\left(-\dfrac{16}{5}\right)\times\left(-6\right)\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\left(-\dfrac{49}{2}+\dfrac{129}{4}+\dfrac{\dfrac{\dfrac{-\dfrac{49}{2}}{\dfrac{61}{6}\times2\times\left(-6\right)\times\dfrac{129}{4}}}{3}}{-9}+\dfrac{3}{2}\times\left(-\dfrac{55}{6}\right)-\dfrac{63}{2}\right)\times\dfrac{\dfrac{\dfrac{-12}{-9}}{-\dfrac{16}{5}}}{-\dfrac{140}{11}}\times\left(-\dfrac{63}{2}\right)\times\left(-\dfrac{16}{5}\right)\times\left(-6\right)=\dfrac{1060111904544}{1427751360}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(-\dfrac{49}{2}+\dfrac{129}{4}+\dfrac{\dfrac{\dfrac{-\dfrac{49}{2}}{\dfrac{61}{3}\times\left(-6\right)\times\dfrac{129}{4}}}{3}}{-9}+\dfrac{3}{2}\times\left(-\dfrac{55}{6}\right)-\dfrac{63}{2}\right)\times\dfrac{\dfrac{\dfrac{-12}{-9}}{-\dfrac{16}{5}}}{-\dfrac{140}{11}}\times\left(-\dfrac{63}{2}\right)\times\left(-\dfrac{16}{5}\right)\times\left(-6\right)\\&=&\left(-\dfrac{49}{2}+\dfrac{129}{4}+\dfrac{\dfrac{\dfrac{-\dfrac{49}{2}}{\left(-122\right)\times\dfrac{129}{4}}}{3}}{-9}+\dfrac{3}{2}\times\left(-\dfrac{55}{6}\right)-\dfrac{63}{2}\right)\times\dfrac{\dfrac{\dfrac{-12}{-9}}{-\dfrac{16}{5}}}{-\dfrac{140}{11}}\times\left(-\dfrac{63}{2}\right)\times\left(-\dfrac{16}{5}\right)\times\left(-6\right)\\&=&\left(-\dfrac{49}{2}+\dfrac{129}{4}+\dfrac{\dfrac{\dfrac{-\dfrac{49}{2}}{-\dfrac{7869}{2}}}{3}}{-9}+\dfrac{3}{2}\times\left(-\dfrac{55}{6}\right)-\dfrac{63}{2}\right)\times\dfrac{\dfrac{\dfrac{-12}{-9}}{-\dfrac{16}{5}}}{-\dfrac{140}{11}}\times\left(-\dfrac{63}{2}\right)\times\left(-\dfrac{16}{5}\right)\times\left(-6\right)\\&=&\left(\dfrac{31}{4}+\dfrac{\dfrac{\dfrac{-\dfrac{49}{2}}{-\dfrac{7869}{2}}}{3}}{-9}+\dfrac{3}{2}\times\left(-\dfrac{55}{6}\right)-\dfrac{63}{2}\right)\times\dfrac{\dfrac{\dfrac{-12}{-9}}{-\dfrac{16}{5}}}{-\dfrac{140}{11}}\times\left(-\dfrac{63}{2}\right)\times\left(-\dfrac{16}{5}\right)\times\left(-6\right)\\&=&\left(\dfrac{31}{4}+\dfrac{\dfrac{\dfrac{49}{7869}}{3}}{-9}+\dfrac{3}{2}\times\left(-\dfrac{55}{6}\right)-\dfrac{63}{2}\right)\times\dfrac{\dfrac{\dfrac{-12}{-9}}{-\dfrac{16}{5}}}{-\dfrac{140}{11}}\times\left(-\dfrac{63}{2}\right)\times\left(-\dfrac{16}{5}\right)\times\left(-6\right)\\&=&\left(\dfrac{31}{4}+\dfrac{\dfrac{49}{23607}}{-9}+\dfrac{3}{2}\times\left(-\dfrac{55}{6}\right)-\dfrac{63}{2}\right)\times\dfrac{\dfrac{\dfrac{-12}{-9}}{-\dfrac{16}{5}}}{-\dfrac{140}{11}}\times\left(-\dfrac{63}{2}\right)\times\left(-\dfrac{16}{5}\right)\times\left(-6\right)\\&=&\left(\dfrac{31}{4}-\dfrac{49}{212463}+\dfrac{3}{2}\times\left(-\dfrac{55}{6}\right)-\dfrac{63}{2}\right)\times\dfrac{\dfrac{\dfrac{-12}{-9}}{-\dfrac{16}{5}}}{-\dfrac{140}{11}}\times\left(-\dfrac{63}{2}\right)\times\left(-\dfrac{16}{5}\right)\times\left(-6\right)\\&=&\left(\dfrac{31}{4}-\dfrac{49}{212463}-\dfrac{55}{4}-\dfrac{63}{2}\right)\times\dfrac{\dfrac{\dfrac{-12}{-9}}{-\dfrac{16}{5}}}{-\dfrac{140}{11}}\times\left(-\dfrac{63}{2}\right)\times\left(-\dfrac{16}{5}\right)\times\left(-6\right)\\&=&\left(\dfrac{6586157}{849852}-\dfrac{55}{4}-\dfrac{63}{2}\right)\times\dfrac{\dfrac{\dfrac{-12}{-9}}{-\dfrac{16}{5}}}{-\dfrac{140}{11}}\times\left(-\dfrac{63}{2}\right)\times\left(-\dfrac{16}{5}\right)\times\left(-6\right)\\&=&\left(-\dfrac{1274827}{212463}-\dfrac{63}{2}\right)\times\dfrac{\dfrac{\dfrac{-12}{-9}}{-\dfrac{16}{5}}}{-\dfrac{140}{11}}\times\left(-\dfrac{63}{2}\right)\times\left(-\dfrac{16}{5}\right)\times\left(-6\right)\\&=&-\dfrac{15934823}{424926}\times\dfrac{\dfrac{\dfrac{-12}{-9}}{-\dfrac{16}{5}}}{-\dfrac{140}{11}}\times\left(-\dfrac{63}{2}\right)\times\left(-\dfrac{16}{5}\right)\times\left(-6\right)\\&=&-\dfrac{15934823}{424926}\times\dfrac{\dfrac{\dfrac{4}{3}}{-\dfrac{16}{5}}}{-\dfrac{140}{11}}\times\left(-\dfrac{63}{2}\right)\times\left(-\dfrac{16}{5}\right)\times\left(-6\right)\\&=&-\dfrac{15934823}{424926}\times\dfrac{-\dfrac{5}{12}}{-\dfrac{140}{11}}\times\left(-\dfrac{63}{2}\right)\times\left(-\dfrac{16}{5}\right)\times\left(-6\right)\\&=&-\dfrac{15934823}{424926}\times\dfrac{11}{336}\times\left(-\dfrac{63}{2}\right)\times\left(-\dfrac{16}{5}\right)\times\left(-6\right)\\&=&-\dfrac{175283053}{142775136}\times\left(-\dfrac{63}{2}\right)\times\left(-\dfrac{16}{5}\right)\times\left(-6\right)\\&=&\left(\dfrac{11042832339}{285550272}\right)\times\left(-\dfrac{16}{5}\right)\times\left(-6\right)\\&=&-\dfrac{176685317424}{1427751360}\times\left(-6\right)\\&=&\dfrac{1060111904544}{1427751360}\\
\end{eqnarray*}