L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Soit \( X=\left(-\dfrac{40}{9}\right)\sqrt{9}\) et \( Y=\dfrac{47}{6}-\left(\dfrac{47}{6}+\dfrac{26}{3}\right)-\left(\left(\left(\dfrac{39}{7}\right)\sqrt{12}\right)-\dfrac{78}{7}-\dfrac{55}{8}-\left(\left(\dfrac{4}{3}\right)\sqrt{12}\right)\right)\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(\left(-\dfrac{40}{9}\right)\sqrt{9}\right)+\left(\dfrac{47}{6}-\left(\dfrac{47}{6}+\dfrac{26}{3}\right)-\left(\left(\left(\dfrac{39}{7}\right)\sqrt{12}\right)-\dfrac{78}{7}-\dfrac{55}{8}-\left(\left(\dfrac{4}{3}\right)\sqrt{12}\right)\right)\right)\\
&=&\left(-\dfrac{40}{3}\right)+\left(\dfrac{47}{6}-\left(\dfrac{47}{6}+\dfrac{26}{3}\right)-\left(\left(\left(\dfrac{78}{7}\right)\sqrt{3}\right)-\dfrac{78}{7}-\dfrac{55}{8}-\left(\left(\dfrac{8}{3}\right)\sqrt{3}\right)\right)\right)\\
&=&-\dfrac{40}{3}+\dfrac{47}{6}-\left(\dfrac{47}{6}+\dfrac{26}{3}\right)-\left(\left(\left(\dfrac{78}{7}\right)\sqrt{3}\right)-\dfrac{78}{7}-\dfrac{55}{8}-\left(\left(\dfrac{8}{3}\right)\sqrt{3}\right)\right)\\
&=&-\dfrac{223}{56}+\left(-\dfrac{178}{21}\right)\sqrt{3}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(-\dfrac{40}{9}\right)\sqrt{9}\right)-\left(\dfrac{47}{6}-\left(\dfrac{47}{6}+\dfrac{26}{3}\right)-\left(\left(\left(\dfrac{39}{7}\right)\sqrt{12}\right)-\dfrac{78}{7}-\dfrac{55}{8}-\left(\left(\dfrac{4}{3}\right)\sqrt{12}\right)\right)\right)\\
&=&\left(-\dfrac{40}{3}\right)-\left(\dfrac{47}{6}-\left(\dfrac{47}{6}+\dfrac{26}{3}\right)-\left(\left(\left(\dfrac{78}{7}\right)\sqrt{3}\right)-\dfrac{78}{7}-\dfrac{55}{8}-\left(\left(\dfrac{8}{3}\right)\sqrt{3}\right)\right)\right)\\
&=&\left(-\dfrac{40}{3}\right)-\left(\dfrac{1571}{168}+\left(-\dfrac{178}{21}\right)\sqrt{3}\right)\\
&=&-\dfrac{40}{3}+-\dfrac{1571}{168}+\left(\dfrac{178}{21}\right)\sqrt{3}\\
&=&-\dfrac{3811}{168}+\left(\dfrac{178}{21}\right)\sqrt{3}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(-\dfrac{40}{9}\right)\sqrt{9}\right)\times\left(\dfrac{47}{6}-\left(\dfrac{47}{6}+\dfrac{26}{3}\right)-\left(\left(\left(\dfrac{39}{7}\right)\sqrt{12}\right)-\dfrac{78}{7}-\dfrac{55}{8}-\left(\left(\dfrac{4}{3}\right)\sqrt{12}\right)\right)\right)\\
&=&\left(-\dfrac{40}{3}\right)\times\left(\dfrac{47}{6}-\left(\dfrac{47}{6}+\dfrac{26}{3}\right)-\left(\left(\left(\dfrac{78}{7}\right)\sqrt{3}\right)-\dfrac{78}{7}-\dfrac{55}{8}-\left(\left(\dfrac{8}{3}\right)\sqrt{3}\right)\right)\right)\\
&=&\left(-\dfrac{40}{3}\right)\left(\dfrac{1571}{168}+\left(-\dfrac{178}{21}\right)\sqrt{3}\right)\\
&=&-\dfrac{7855}{63}+\left(\dfrac{7120}{63}\right)\sqrt{3}\\
&=&-\dfrac{7855}{63}+\left(\dfrac{7120}{63}\right)\sqrt{3}\\
\end{eqnarray*}