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 \( X=-\dfrac{67}{5}-\left(0-\left(\left(\dfrac{69}{5}\right)\sqrt{27}\right)\right)\) et \( Y=\left(\dfrac{79}{5}\right)\sqrt{9}\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(-\dfrac{67}{5}-\left(0-\left(\left(\dfrac{69}{5}\right)\sqrt{27}\right)\right)\right)+\left(\left(\dfrac{79}{5}\right)\sqrt{9}\right)\\
&=&\left(-\dfrac{67}{5}-\left(0-\left(\left(\dfrac{207}{5}\right)\sqrt{3}\right)\right)\right)+\left(\dfrac{237}{5}\right)\\
&=&-\dfrac{67}{5}-\left(0-\left(\left(\dfrac{207}{5}\right)\sqrt{3}\right)\right)+\dfrac{237}{5}\\
&=&34+\left(\dfrac{207}{5}\right)\sqrt{3}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(-\dfrac{67}{5}-\left(0-\left(\left(\dfrac{69}{5}\right)\sqrt{27}\right)\right)\right)-\left(\left(\dfrac{79}{5}\right)\sqrt{9}\right)\\
&=&\left(-\dfrac{67}{5}-\left(0-\left(\left(\dfrac{207}{5}\right)\sqrt{3}\right)\right)\right)-\left(\dfrac{237}{5}\right)\\
&=&\left(-\dfrac{67}{5}+\left(\dfrac{207}{5}\right)\sqrt{3}\right)-\left(\dfrac{237}{5}\right)\\
&=&-\dfrac{67}{5}+\left(\dfrac{207}{5}\right)\sqrt{3}+-\dfrac{237}{5}\\
&=&-\dfrac{304}{5}+\left(\dfrac{207}{5}\right)\sqrt{3}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(-\dfrac{67}{5}-\left(0-\left(\left(\dfrac{69}{5}\right)\sqrt{27}\right)\right)\right)\times\left(\left(\dfrac{79}{5}\right)\sqrt{9}\right)\\
&=&\left(-\dfrac{67}{5}-\left(0-\left(\left(\dfrac{207}{5}\right)\sqrt{3}\right)\right)\right)\times\left(\dfrac{237}{5}\right)\\
&=&\left(-\dfrac{67}{5}+\left(\dfrac{207}{5}\right)\sqrt{3}\right)\left(\dfrac{237}{5}\right)\\
&=&-\dfrac{15879}{25}+\left(\dfrac{49059}{25}\right)\sqrt{3}\\
&=&-\dfrac{15879}{25}+\left(\dfrac{49059}{25}\right)\sqrt{3}\\
\end{eqnarray*}