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
Soit \( X=\left(\left(\dfrac{38}{7}\right)\sqrt{28}\right)-\left(\left(\dfrac{62}{7}\right)\sqrt{63}\right)-\left(\left(\dfrac{65}{7}\right)\sqrt{63}+\left(-\dfrac{7}{4}\right)\sqrt{63}+\left(-\dfrac{81}{5}\right)\sqrt{49}+\left(-7\right)\sqrt{175}-\dfrac{51}{7}\right)-\left(\left(\left(-\dfrac{37}{3}\right)\sqrt{63}\right)-\left(\left(\dfrac{64}{9}\right)\sqrt{175}\right)-\left(\left(\dfrac{1}{2}\right)\sqrt{63}\right)\right)\) et \( Y=\left(-\dfrac{37}{2}\right)\sqrt{49}\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(\left(\left(\dfrac{38}{7}\right)\sqrt{28}\right)-\left(\left(\dfrac{62}{7}\right)\sqrt{63}\right)-\left(\left(\dfrac{65}{7}\right)\sqrt{63}+\left(-\dfrac{7}{4}\right)\sqrt{63}+\left(-\dfrac{81}{5}\right)\sqrt{49}+\left(-7\right)\sqrt{175}-\dfrac{51}{7}\right)-\left(\left(\left(-\dfrac{37}{3}\right)\sqrt{63}\right)-\left(\left(\dfrac{64}{9}\right)\sqrt{175}\right)-\left(\left(\dfrac{1}{2}\right)\sqrt{63}\right)\right)\right)+\left(\left(-\dfrac{37}{2}\right)\sqrt{49}\right)\\
&=&\left(\left(\left(\dfrac{76}{7}\right)\sqrt{7}\right)-\left(\left(\dfrac{186}{7}\right)\sqrt{7}\right)-\left(\left(\dfrac{195}{7}\right)\sqrt{7}+\left(-\dfrac{21}{4}\right)\sqrt{7}-\dfrac{567}{5}+\left(-35\right)\sqrt{7}-\dfrac{51}{7}\right)-\left(\left(\left(-37\right)\sqrt{7}\right)-\left(\left(\dfrac{320}{9}\right)\sqrt{7}\right)-\left(\left(\dfrac{3}{2}\right)\sqrt{7}\right)\right)\right)+\left(-\dfrac{259}{2}\right)\\
&=&\left(\left(\dfrac{76}{7}\right)\sqrt{7}\right)-\left(\left(\dfrac{186}{7}\right)\sqrt{7}\right)-\left(\left(\dfrac{195}{7}\right)\sqrt{7}+\left(-\dfrac{21}{4}\right)\sqrt{7}-\dfrac{567}{5}+\left(-35\right)\sqrt{7}-\dfrac{51}{7}\right)-\left(\left(\left(-37\right)\sqrt{7}\right)-\left(\left(\dfrac{320}{9}\right)\sqrt{7}\right)-\left(\left(\dfrac{3}{2}\right)\sqrt{7}\right)\right)-\dfrac{259}{2}\\
&=&\left(\dfrac{17825}{252}\right)\sqrt{7}-\dfrac{617}{70}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\left(\dfrac{38}{7}\right)\sqrt{28}\right)-\left(\left(\dfrac{62}{7}\right)\sqrt{63}\right)-\left(\left(\dfrac{65}{7}\right)\sqrt{63}+\left(-\dfrac{7}{4}\right)\sqrt{63}+\left(-\dfrac{81}{5}\right)\sqrt{49}+\left(-7\right)\sqrt{175}-\dfrac{51}{7}\right)-\left(\left(\left(-\dfrac{37}{3}\right)\sqrt{63}\right)-\left(\left(\dfrac{64}{9}\right)\sqrt{175}\right)-\left(\left(\dfrac{1}{2}\right)\sqrt{63}\right)\right)\right)-\left(\left(-\dfrac{37}{2}\right)\sqrt{49}\right)\\
&=&\left(\left(\left(\dfrac{76}{7}\right)\sqrt{7}\right)-\left(\left(\dfrac{186}{7}\right)\sqrt{7}\right)-\left(\left(\dfrac{195}{7}\right)\sqrt{7}+\left(-\dfrac{21}{4}\right)\sqrt{7}-\dfrac{567}{5}+\left(-35\right)\sqrt{7}-\dfrac{51}{7}\right)-\left(\left(\left(-37\right)\sqrt{7}\right)-\left(\left(\dfrac{320}{9}\right)\sqrt{7}\right)-\left(\left(\dfrac{3}{2}\right)\sqrt{7}\right)\right)\right)-\left(-\dfrac{259}{2}\right)\\
&=&\left(\left(\dfrac{17825}{252}\right)\sqrt{7}+\dfrac{4224}{35}\right)-\left(-\dfrac{259}{2}\right)\\
&=&\left(\dfrac{17825}{252}\right)\sqrt{7}+\dfrac{4224}{35}+\dfrac{259}{2}\\
&=&\left(\dfrac{17825}{252}\right)\sqrt{7}+\dfrac{17513}{70}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\left(\dfrac{38}{7}\right)\sqrt{28}\right)-\left(\left(\dfrac{62}{7}\right)\sqrt{63}\right)-\left(\left(\dfrac{65}{7}\right)\sqrt{63}+\left(-\dfrac{7}{4}\right)\sqrt{63}+\left(-\dfrac{81}{5}\right)\sqrt{49}+\left(-7\right)\sqrt{175}-\dfrac{51}{7}\right)-\left(\left(\left(-\dfrac{37}{3}\right)\sqrt{63}\right)-\left(\left(\dfrac{64}{9}\right)\sqrt{175}\right)-\left(\left(\dfrac{1}{2}\right)\sqrt{63}\right)\right)\right)\times\left(\left(-\dfrac{37}{2}\right)\sqrt{49}\right)\\
&=&\left(\left(\left(\dfrac{76}{7}\right)\sqrt{7}\right)-\left(\left(\dfrac{186}{7}\right)\sqrt{7}\right)-\left(\left(\dfrac{195}{7}\right)\sqrt{7}+\left(-\dfrac{21}{4}\right)\sqrt{7}-\dfrac{567}{5}+\left(-35\right)\sqrt{7}-\dfrac{51}{7}\right)-\left(\left(\left(-37\right)\sqrt{7}\right)-\left(\left(\dfrac{320}{9}\right)\sqrt{7}\right)-\left(\left(\dfrac{3}{2}\right)\sqrt{7}\right)\right)\right)\times\left(-\dfrac{259}{2}\right)\\
&=&\left(\left(\dfrac{17825}{252}\right)\sqrt{7}+\dfrac{4224}{35}\right)\left(-\dfrac{259}{2}\right)\\
&=&\left(-\dfrac{659525}{72}\right)\sqrt{7}-\dfrac{78144}{5}\\
&=&\left(-\dfrac{659525}{72}\right)\sqrt{7}-\dfrac{78144}{5}\\
\end{eqnarray*}