L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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Exercice
Soit \( X=\left(-\dfrac{73}{9}\right)\sqrt{28}+\left(\left(-\dfrac{25}{7}\right)\sqrt{49}\right)-\left(\left(\dfrac{20}{3}\right)\sqrt{28}\right)+\left(\dfrac{68}{5}\right)\sqrt{175}+\left(0\right)\sqrt{49}+\left(-\dfrac{33}{2}\right)\sqrt{28}+\left(-7\right)\sqrt{49}+\left(-\dfrac{18}{7}\right)\sqrt{63}+\left(-\dfrac{35}{4}\right)\sqrt{28}-\dfrac{41}{5}+\left(\dfrac{19}{8}\right)\sqrt{63}\) et \( Y=\left(1\right)\sqrt{63}-\dfrac{67}{4}+\left(\dfrac{47}{9}\right)\sqrt{28}+\left(-\dfrac{55}{6}\right)\sqrt{28}+\left(-\dfrac{72}{7}\right)\sqrt{49}+\left(-\dfrac{59}{3}\right)\sqrt{63}+\left(-\dfrac{34}{3}\right)\sqrt{28}+\left(\dfrac{79}{2}\right)\sqrt{28}+\left(1\right)\sqrt{63}\) . 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{73}{9}\right)\sqrt{28}+\left(\left(-\dfrac{25}{7}\right)\sqrt{49}\right)-\left(\left(\dfrac{20}{3}\right)\sqrt{28}\right)+\left(\dfrac{68}{5}\right)\sqrt{175}+\left(0\right)\sqrt{49}+\left(-\dfrac{33}{2}\right)\sqrt{28}+\left(-7\right)\sqrt{49}+\left(-\dfrac{18}{7}\right)\sqrt{63}+\left(-\dfrac{35}{4}\right)\sqrt{28}-\dfrac{41}{5}+\left(\dfrac{19}{8}\right)\sqrt{63}\right)+\left(\left(1\right)\sqrt{63}-\dfrac{67}{4}+\left(\dfrac{47}{9}\right)\sqrt{28}+\left(-\dfrac{55}{6}\right)\sqrt{28}+\left(-\dfrac{72}{7}\right)\sqrt{49}+\left(-\dfrac{59}{3}\right)\sqrt{63}+\left(-\dfrac{34}{3}\right)\sqrt{28}+\left(\dfrac{79}{2}\right)\sqrt{28}+\left(1\right)\sqrt{63}\right)\\
&=&\left(\left(-\dfrac{146}{9}\right)\sqrt{7}-25-\left(\left(\dfrac{40}{3}\right)\sqrt{7}\right)+\left(68\right)\sqrt{7}+0+\left(-33\right)\sqrt{7}-49+\left(-\dfrac{54}{7}\right)\sqrt{7}+\left(-\dfrac{35}{2}\right)\sqrt{7}-\dfrac{41}{5}+\left(\dfrac{57}{8}\right)\sqrt{7}\right)+\left(\left(3\right)\sqrt{7}-\dfrac{67}{4}+\left(\dfrac{94}{9}\right)\sqrt{7}+\left(-\dfrac{55}{3}\right)\sqrt{7}-72+\left(-59\right)\sqrt{7}+\left(-\dfrac{68}{3}\right)\sqrt{7}+\left(79\right)\sqrt{7}+\left(3\right)\sqrt{7}\right)\\
&=&\left(-\dfrac{146}{9}\right)\sqrt{7}-25-\left(\left(\dfrac{40}{3}\right)\sqrt{7}\right)+\left(68\right)\sqrt{7}+0+\left(-33\right)\sqrt{7}-49+\left(-\dfrac{54}{7}\right)\sqrt{7}+\left(-\dfrac{35}{2}\right)\sqrt{7}-\dfrac{41}{5}+\left(\dfrac{57}{8}\right)\sqrt{7}+\left(3\right)\sqrt{7}-\dfrac{67}{4}+\left(\dfrac{94}{9}\right)\sqrt{7}+\left(-\dfrac{55}{3}\right)\sqrt{7}-72+\left(-59\right)\sqrt{7}+\left(-\dfrac{68}{3}\right)\sqrt{7}+\left(79\right)\sqrt{7}+\left(3\right)\sqrt{7}\\
&=&\left(-\dfrac{8669}{504}\right)\sqrt{7}-\dfrac{3419}{20}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(-\dfrac{73}{9}\right)\sqrt{28}+\left(\left(-\dfrac{25}{7}\right)\sqrt{49}\right)-\left(\left(\dfrac{20}{3}\right)\sqrt{28}\right)+\left(\dfrac{68}{5}\right)\sqrt{175}+\left(0\right)\sqrt{49}+\left(-\dfrac{33}{2}\right)\sqrt{28}+\left(-7\right)\sqrt{49}+\left(-\dfrac{18}{7}\right)\sqrt{63}+\left(-\dfrac{35}{4}\right)\sqrt{28}-\dfrac{41}{5}+\left(\dfrac{19}{8}\right)\sqrt{63}\right)-\left(\left(1\right)\sqrt{63}-\dfrac{67}{4}+\left(\dfrac{47}{9}\right)\sqrt{28}+\left(-\dfrac{55}{6}\right)\sqrt{28}+\left(-\dfrac{72}{7}\right)\sqrt{49}+\left(-\dfrac{59}{3}\right)\sqrt{63}+\left(-\dfrac{34}{3}\right)\sqrt{28}+\left(\dfrac{79}{2}\right)\sqrt{28}+\left(1\right)\sqrt{63}\right)\\
&=&\left(\left(-\dfrac{146}{9}\right)\sqrt{7}-25-\left(\left(\dfrac{40}{3}\right)\sqrt{7}\right)+\left(68\right)\sqrt{7}+0+\left(-33\right)\sqrt{7}-49+\left(-\dfrac{54}{7}\right)\sqrt{7}+\left(-\dfrac{35}{2}\right)\sqrt{7}-\dfrac{41}{5}+\left(\dfrac{57}{8}\right)\sqrt{7}\right)-\left(\left(3\right)\sqrt{7}-\dfrac{67}{4}+\left(\dfrac{94}{9}\right)\sqrt{7}+\left(-\dfrac{55}{3}\right)\sqrt{7}-72+\left(-59\right)\sqrt{7}+\left(-\dfrac{68}{3}\right)\sqrt{7}+\left(79\right)\sqrt{7}+\left(3\right)\sqrt{7}\right)\\
&=&\left(\left(-\dfrac{6373}{504}\right)\sqrt{7}-\dfrac{411}{5}\right)-\left(\left(-\dfrac{41}{9}\right)\sqrt{7}-\dfrac{355}{4}\right)\\
&=&\left(-\dfrac{6373}{504}\right)\sqrt{7}-\dfrac{411}{5}+\left(\dfrac{41}{9}\right)\sqrt{7}+\dfrac{355}{4}\\
&=&\left(-\dfrac{453}{56}\right)\sqrt{7}+\dfrac{131}{20}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(-\dfrac{73}{9}\right)\sqrt{28}+\left(\left(-\dfrac{25}{7}\right)\sqrt{49}\right)-\left(\left(\dfrac{20}{3}\right)\sqrt{28}\right)+\left(\dfrac{68}{5}\right)\sqrt{175}+\left(0\right)\sqrt{49}+\left(-\dfrac{33}{2}\right)\sqrt{28}+\left(-7\right)\sqrt{49}+\left(-\dfrac{18}{7}\right)\sqrt{63}+\left(-\dfrac{35}{4}\right)\sqrt{28}-\dfrac{41}{5}+\left(\dfrac{19}{8}\right)\sqrt{63}\right)\times\left(\left(1\right)\sqrt{63}-\dfrac{67}{4}+\left(\dfrac{47}{9}\right)\sqrt{28}+\left(-\dfrac{55}{6}\right)\sqrt{28}+\left(-\dfrac{72}{7}\right)\sqrt{49}+\left(-\dfrac{59}{3}\right)\sqrt{63}+\left(-\dfrac{34}{3}\right)\sqrt{28}+\left(\dfrac{79}{2}\right)\sqrt{28}+\left(1\right)\sqrt{63}\right)\\
&=&\left(\left(-\dfrac{146}{9}\right)\sqrt{7}-25-\left(\left(\dfrac{40}{3}\right)\sqrt{7}\right)+\left(68\right)\sqrt{7}+0+\left(-33\right)\sqrt{7}-49+\left(-\dfrac{54}{7}\right)\sqrt{7}+\left(-\dfrac{35}{2}\right)\sqrt{7}-\dfrac{41}{5}+\left(\dfrac{57}{8}\right)\sqrt{7}\right)\times\left(\left(3\right)\sqrt{7}-\dfrac{67}{4}+\left(\dfrac{94}{9}\right)\sqrt{7}+\left(-\dfrac{55}{3}\right)\sqrt{7}-72+\left(-59\right)\sqrt{7}+\left(-\dfrac{68}{3}\right)\sqrt{7}+\left(79\right)\sqrt{7}+\left(3\right)\sqrt{7}\right)\\
&=&\left(\left(-\dfrac{6373}{504}\right)\sqrt{7}-\dfrac{411}{5}\right)\left(\left(-\dfrac{41}{9}\right)\sqrt{7}-\dfrac{355}{4}\right)\\
&=&\left(\dfrac{261293}{4536}\right)\sqrt{49}+\left(\dfrac{15086699}{10080}\right)\sqrt{7}+\dfrac{29181}{4}\\
&=&\dfrac{4988615}{648}+\left(\dfrac{15086699}{10080}\right)\sqrt{7}\\
\end{eqnarray*}