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Exercice

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 \[\dfrac{-19}{\dfrac{61}{4}\times\left(-3\right)\times\left(19+\dfrac{169}{8}-\left(\dfrac{\dfrac{\dfrac{276}{19}}{-18}}{\left(-13\right)\times\left(-5\right)}-\dfrac{\dfrac{\dfrac{-\dfrac{169}{8}}{\dfrac{193}{13}}}{\dfrac{61}{4}}}{-18}\times\left(\dfrac{276}{19}+11\right)\times\dfrac{193}{13}+1\right)-\dfrac{\dfrac{\dfrac{\dfrac{105}{8}}{\dfrac{193}{13}}}{\dfrac{\dfrac{\dfrac{\dfrac{118}{13}}{-9}}{-15}}{-\dfrac{169}{8}}\times\dfrac{61}{4}\times19}}{-\dfrac{10}{3}}\right)}\]
Cliquer ici pour afficher la solution

Exercice


On a \( X=\dfrac{-19}{\dfrac{61}{4}\times\left(-3\right)\times\left(19+\dfrac{169}{8}-\left(\dfrac{\dfrac{\dfrac{276}{19}}{-18}}{\left(-13\right)\times\left(-5\right)}-\dfrac{\dfrac{\dfrac{-\dfrac{169}{8}}{\dfrac{193}{13}}}{\dfrac{61}{4}}}{-18}\times\left(\dfrac{276}{19}+11\right)\times\dfrac{193}{13}+1\right)-\dfrac{\dfrac{\dfrac{\dfrac{105}{8}}{\dfrac{193}{13}}}{\dfrac{\dfrac{\dfrac{\dfrac{118}{13}}{-9}}{-15}}{-\dfrac{169}{8}}\times\dfrac{61}{4}\times19}}{-\dfrac{10}{3}}\right)}=\dfrac{1740947265565747200}{1.7109419389914E+20}\) . Voici le détail : \begin{eqnarray*} X &=&\dfrac{-19}{\dfrac{61}{4}\times\left(-3\right)\times\left(19+\dfrac{169}{8}-\left(\dfrac{\dfrac{\dfrac{276}{19}}{-18}}{65}-\dfrac{\dfrac{\dfrac{-\dfrac{169}{8}}{\dfrac{193}{13}}}{\dfrac{61}{4}}}{-18}\times\left(\dfrac{276}{19}+11\right)\times\dfrac{193}{13}+1\right)-\dfrac{\dfrac{\dfrac{\dfrac{105}{8}}{\dfrac{193}{13}}}{\dfrac{\dfrac{\dfrac{\dfrac{118}{13}}{-9}}{-15}}{-\dfrac{169}{8}}\times\dfrac{61}{4}\times19}}{-\dfrac{10}{3}}\right)}\\&=&\dfrac{-19}{\dfrac{61}{4}\times\left(-3\right)\times\left(19+\dfrac{169}{8}-\left(\dfrac{\dfrac{\dfrac{276}{19}}{-18}}{65}-\dfrac{\dfrac{-\dfrac{2197}{1544}}{\dfrac{61}{4}}}{-18}\times\left(\dfrac{276}{19}+11\right)\times\dfrac{193}{13}+1\right)-\dfrac{\dfrac{\dfrac{\dfrac{105}{8}}{\dfrac{193}{13}}}{\dfrac{\dfrac{\dfrac{\dfrac{118}{13}}{-9}}{-15}}{-\dfrac{169}{8}}\times\dfrac{61}{4}\times19}}{-\dfrac{10}{3}}\right)}\\&=&\dfrac{-19}{\dfrac{61}{4}\times\left(-3\right)\times\left(19+\dfrac{169}{8}-\left(\dfrac{\dfrac{\dfrac{276}{19}}{-18}}{65}-\dfrac{-\dfrac{2197}{23546}}{-18}\times\left(\dfrac{276}{19}+11\right)\times\dfrac{193}{13}+1\right)-\dfrac{\dfrac{\dfrac{\dfrac{105}{8}}{\dfrac{193}{13}}}{\dfrac{\dfrac{\dfrac{\dfrac{118}{13}}{-9}}{-15}}{-\dfrac{169}{8}}\times\dfrac{61}{4}\times19}}{-\dfrac{10}{3}}\right)}\\&=&\dfrac{-19}{\dfrac{61}{4}\times\left(-3\right)\times\left(19+\dfrac{169}{8}-\left(\dfrac{\dfrac{\dfrac{276}{19}}{-18}}{65}-\dfrac{2197}{423828}\times\left(\dfrac{276}{19}+11\right)\times\dfrac{193}{13}+1\right)-\dfrac{\dfrac{\dfrac{\dfrac{105}{8}}{\dfrac{193}{13}}}{\dfrac{\dfrac{\dfrac{\dfrac{118}{13}}{-9}}{-15}}{-\dfrac{169}{8}}\times\dfrac{61}{4}\times19}}{-\dfrac{10}{3}}\right)}\\&=&\dfrac{-19}{\dfrac{61}{4}\times\left(-3\right)\times\left(19+\dfrac{169}{8}-\left(\dfrac{\dfrac{\dfrac{276}{19}}{-18}}{65}-\dfrac{2197}{423828}\times\dfrac{485}{19}\times\dfrac{193}{13}+1\right)-\dfrac{\dfrac{\dfrac{\dfrac{105}{8}}{\dfrac{193}{13}}}{\dfrac{\dfrac{\dfrac{\dfrac{118}{13}}{-9}}{-15}}{-\dfrac{169}{8}}\times\dfrac{61}{4}\times19}}{-\dfrac{10}{3}}\right)}\\&=&\dfrac{-19}{\dfrac{61}{4}\times\left(-3\right)\times\left(19+\dfrac{169}{8}-\left(\dfrac{\dfrac{\dfrac{276}{19}}{-18}}{65}-\dfrac{2197}{423828}\times\dfrac{485}{19}\times\dfrac{193}{13}+1\right)-\dfrac{\dfrac{\dfrac{\dfrac{105}{8}}{\dfrac{193}{13}}}{\dfrac{\dfrac{-\dfrac{118}{117}}{-15}}{-\dfrac{169}{8}}\times\dfrac{61}{4}\times19}}{-\dfrac{10}{3}}\right)}\\&=&\dfrac{-19}{\dfrac{61}{4}\times\left(-3\right)\times\left(19+\dfrac{169}{8}-\left(\dfrac{\dfrac{\dfrac{276}{19}}{-18}}{65}-\dfrac{2197}{423828}\times\dfrac{485}{19}\times\dfrac{193}{13}+1\right)-\dfrac{\dfrac{\dfrac{\dfrac{105}{8}}{\dfrac{193}{13}}}{\dfrac{\dfrac{118}{1755}}{-\dfrac{169}{8}}\times\dfrac{61}{4}\times19}}{-\dfrac{10}{3}}\right)}\\&=&\dfrac{-19}{\dfrac{61}{4}\times\left(-3\right)\times\left(19+\dfrac{169}{8}-\left(\dfrac{\dfrac{\dfrac{276}{19}}{-18}}{65}-\dfrac{2197}{423828}\times\dfrac{485}{19}\times\dfrac{193}{13}+1\right)-\dfrac{\dfrac{\dfrac{\dfrac{105}{8}}{\dfrac{193}{13}}}{\left(-\dfrac{944}{296595}\right)\times\dfrac{61}{4}\times19}}{-\dfrac{10}{3}}\right)}\\&=&\dfrac{-19}{\dfrac{61}{4}\times\left(-3\right)\times\left(19+\dfrac{169}{8}-\left(\dfrac{-\dfrac{46}{57}}{65}-\dfrac{2197}{423828}\times\dfrac{485}{19}\times\dfrac{193}{13}+1\right)-\dfrac{\dfrac{\dfrac{\dfrac{105}{8}}{\dfrac{193}{13}}}{\left(-\dfrac{944}{296595}\right)\times\dfrac{61}{4}\times19}}{-\dfrac{10}{3}}\right)}\\&=&\dfrac{-19}{\dfrac{61}{4}\times\left(-3\right)\times\left(19+\dfrac{169}{8}-\left(-\dfrac{46}{3705}-\dfrac{2197}{423828}\times\dfrac{485}{19}\times\dfrac{193}{13}+1\right)-\dfrac{\dfrac{\dfrac{\dfrac{105}{8}}{\dfrac{193}{13}}}{\left(-\dfrac{944}{296595}\right)\times\dfrac{61}{4}\times19}}{-\dfrac{10}{3}}\right)}\\&=&\dfrac{-19}{\dfrac{61}{4}\times\left(-3\right)\times\left(19+\dfrac{169}{8}-\left(-\dfrac{46}{3705}-\dfrac{1065545}{8052732}\times\dfrac{193}{13}+1\right)-\dfrac{\dfrac{\dfrac{\dfrac{105}{8}}{\dfrac{193}{13}}}{\left(-\dfrac{944}{296595}\right)\times\dfrac{61}{4}\times19}}{-\dfrac{10}{3}}\right)}\\&=&\dfrac{-19}{\dfrac{61}{4}\times\left(-3\right)\times\left(19+\dfrac{169}{8}-\left(-\dfrac{46}{3705}-\dfrac{81965}{41724}+1\right)-\dfrac{\dfrac{\dfrac{\dfrac{105}{8}}{\dfrac{193}{13}}}{\left(-\dfrac{944}{296595}\right)\times\dfrac{61}{4}\times19}}{-\dfrac{10}{3}}\right)}\\&=&\dfrac{-19}{\dfrac{61}{4}\times\left(-3\right)\times\left(19+\dfrac{169}{8}-\left(-\dfrac{46}{3705}-\dfrac{81965}{41724}+1\right)-\dfrac{\dfrac{\dfrac{\dfrac{105}{8}}{\dfrac{193}{13}}}{\left(-\dfrac{14396}{296595}\right)\times19}}{-\dfrac{10}{3}}\right)}\\&=&\dfrac{-19}{\dfrac{61}{4}\times\left(-3\right)\times\left(19+\dfrac{169}{8}-\left(-\dfrac{46}{3705}-\dfrac{81965}{41724}+1\right)-\dfrac{\dfrac{\dfrac{\dfrac{105}{8}}{\dfrac{193}{13}}}{-\dfrac{273524}{296595}}}{-\dfrac{10}{3}}\right)}\\&=&\dfrac{-19}{\dfrac{61}{4}\times\left(-3\right)\times\left(19+\dfrac{169}{8}-\left(-\dfrac{5361397}{2712060}+1\right)-\dfrac{\dfrac{\dfrac{\dfrac{105}{8}}{\dfrac{193}{13}}}{-\dfrac{273524}{296595}}}{-\dfrac{10}{3}}\right)}\\&=&\dfrac{-19}{\dfrac{61}{4}\times\left(-3\right)\times\left(19+\dfrac{169}{8}+\dfrac{2649337}{2712060}-\dfrac{\dfrac{\dfrac{\dfrac{105}{8}}{\dfrac{193}{13}}}{-\dfrac{273524}{296595}}}{-\dfrac{10}{3}}\right)}\\&=&\dfrac{-19}{\dfrac{61}{4}\times\left(-3\right)\times\left(19+\dfrac{169}{8}+\dfrac{2649337}{2712060}-\dfrac{\dfrac{\dfrac{1365}{1544}}{-\dfrac{273524}{296595}}}{-\dfrac{10}{3}}\right)}\\&=&\dfrac{-19}{\dfrac{61}{4}\times\left(-3\right)\times\left(19+\dfrac{169}{8}+\dfrac{2649337}{2712060}-\dfrac{-\dfrac{404852175}{422321056}}{-\dfrac{10}{3}}\right)}\\&=&\dfrac{-19}{\dfrac{61}{4}\times\left(-3\right)\times\left(19+\dfrac{169}{8}+\dfrac{2649337}{2712060}-\dfrac{1214556525}{4223210560}\right)}\\&=&\dfrac{-19}{\dfrac{61}{4}\times\left(-3\right)\times\left(\dfrac{321}{8}+\dfrac{2649337}{2712060}-\dfrac{1214556525}{4223210560}\right)}\\&=&\dfrac{-19}{\dfrac{61}{4}\times\left(-3\right)\times\left(\dfrac{222941489}{5424120}-\dfrac{1214556525}{4223210560}\right)}\\&=&\dfrac{-19}{\dfrac{61}{4}\times\left(-3\right)\times\dfrac{934940950268540840}{22907200862707200}}\\&=&\dfrac{-19}{\left(-\dfrac{183}{4}\right)\times\dfrac{934940950268540840}{22907200862707200}}\\&=&\dfrac{-19}{-\dfrac{1.7109419389914E+20}{91628803450828800}}\\&=&\dfrac{1740947265565747200}{1.7109419389914E+20}\\ \end{eqnarray*}