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 \( X=\dfrac{79}{5}-\left(\left(\left(-\dfrac{31}{2}\right)\sqrt{9}\right)-\left(\left(-\dfrac{31}{2}\right)\sqrt{75}\right)-\left(\left(-\dfrac{36}{5}\right)\sqrt{12}\right)\right)\) et \( Y=\left(-\dfrac{46}{7}\right)\sqrt{27}\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(\dfrac{79}{5}-\left(\left(\left(-\dfrac{31}{2}\right)\sqrt{9}\right)-\left(\left(-\dfrac{31}{2}\right)\sqrt{75}\right)-\left(\left(-\dfrac{36}{5}\right)\sqrt{12}\right)\right)\right)+\left(\left(-\dfrac{46}{7}\right)\sqrt{27}\right)\\
&=&\left(\dfrac{79}{5}-\left(-\dfrac{93}{2}-\left(\left(-\dfrac{155}{2}\right)\sqrt{3}\right)-\left(\left(-\dfrac{72}{5}\right)\sqrt{3}\right)\right)\right)+\left(\left(-\dfrac{138}{7}\right)\sqrt{3}\right)\\
&=&\dfrac{79}{5}-\left(-\dfrac{93}{2}-\left(\left(-\dfrac{155}{2}\right)\sqrt{3}\right)-\left(\left(-\dfrac{72}{5}\right)\sqrt{3}\right)\right)+\left(-\dfrac{138}{7}\right)\sqrt{3}\\
&=&\dfrac{623}{10}+\left(-\dfrac{7813}{70}\right)\sqrt{3}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\dfrac{79}{5}-\left(\left(\left(-\dfrac{31}{2}\right)\sqrt{9}\right)-\left(\left(-\dfrac{31}{2}\right)\sqrt{75}\right)-\left(\left(-\dfrac{36}{5}\right)\sqrt{12}\right)\right)\right)-\left(\left(-\dfrac{46}{7}\right)\sqrt{27}\right)\\
&=&\left(\dfrac{79}{5}-\left(-\dfrac{93}{2}-\left(\left(-\dfrac{155}{2}\right)\sqrt{3}\right)-\left(\left(-\dfrac{72}{5}\right)\sqrt{3}\right)\right)\right)-\left(\left(-\dfrac{138}{7}\right)\sqrt{3}\right)\\
&=&\left(\dfrac{623}{10}+\left(-\dfrac{919}{10}\right)\sqrt{3}\right)-\left(\left(-\dfrac{138}{7}\right)\sqrt{3}\right)\\
&=&\dfrac{623}{10}+\left(-\dfrac{919}{10}\right)\sqrt{3}+\left(\dfrac{138}{7}\right)\sqrt{3}\\
&=&\dfrac{623}{10}+\left(-\dfrac{5053}{70}\right)\sqrt{3}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\dfrac{79}{5}-\left(\left(\left(-\dfrac{31}{2}\right)\sqrt{9}\right)-\left(\left(-\dfrac{31}{2}\right)\sqrt{75}\right)-\left(\left(-\dfrac{36}{5}\right)\sqrt{12}\right)\right)\right)\times\left(\left(-\dfrac{46}{7}\right)\sqrt{27}\right)\\
&=&\left(\dfrac{79}{5}-\left(-\dfrac{93}{2}-\left(\left(-\dfrac{155}{2}\right)\sqrt{3}\right)-\left(\left(-\dfrac{72}{5}\right)\sqrt{3}\right)\right)\right)\times\left(\left(-\dfrac{138}{7}\right)\sqrt{3}\right)\\
&=&\left(\dfrac{623}{10}+\left(-\dfrac{919}{10}\right)\sqrt{3}\right)\left(\left(-\dfrac{138}{7}\right)\sqrt{3}\right)\\
&=&\left(-\dfrac{6141}{5}\right)\sqrt{3}+\left(\dfrac{63411}{35}\right)\sqrt{9}\\
&=&\left(-\dfrac{6141}{5}\right)\sqrt{3}+\dfrac{190233}{35}\\
\end{eqnarray*}