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 \( X=\dfrac{45}{7}-\left(\left(-\dfrac{11}{6}\right)\sqrt{20}\right)\) et \( Y=\left(\left(\left(7\right)\sqrt{45}\right)-\dfrac{33}{4}+\dfrac{37}{5}\right)-4-\left(\left(0\right)\sqrt{25}\right)\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(\dfrac{45}{7}-\left(\left(-\dfrac{11}{6}\right)\sqrt{20}\right)\right)+\left(\left(\left(\left(7\right)\sqrt{45}\right)-\dfrac{33}{4}+\dfrac{37}{5}\right)-4-\left(\left(0\right)\sqrt{25}\right)\right)\\
&=&\left(\dfrac{45}{7}-\left(\left(-\dfrac{11}{3}\right)\sqrt{5}\right)\right)+\left(\left(\left(\left(21\right)\sqrt{5}\right)-\dfrac{33}{4}+\dfrac{37}{5}\right)-4-0\right)\\
&=&\dfrac{45}{7}-\left(\left(-\dfrac{11}{3}\right)\sqrt{5}\right)+\left(\left(\left(21\right)\sqrt{5}\right)-\dfrac{33}{4}+\dfrac{37}{5}\right)-4-0\\
&=&\dfrac{221}{140}+\left(\dfrac{74}{3}\right)\sqrt{5}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\dfrac{45}{7}-\left(\left(-\dfrac{11}{6}\right)\sqrt{20}\right)\right)-\left(\left(\left(\left(7\right)\sqrt{45}\right)-\dfrac{33}{4}+\dfrac{37}{5}\right)-4-\left(\left(0\right)\sqrt{25}\right)\right)\\
&=&\left(\dfrac{45}{7}-\left(\left(-\dfrac{11}{3}\right)\sqrt{5}\right)\right)-\left(\left(\left(\left(21\right)\sqrt{5}\right)-\dfrac{33}{4}+\dfrac{37}{5}\right)-4-0\right)\\
&=&\left(\dfrac{45}{7}+\left(\dfrac{11}{3}\right)\sqrt{5}\right)-\left(\left(21\right)\sqrt{5}-\dfrac{97}{20}\right)\\
&=&\dfrac{45}{7}+\left(\dfrac{11}{3}\right)\sqrt{5}+\left(-21\right)\sqrt{5}+\dfrac{97}{20}\\
&=&\dfrac{1579}{140}+\left(-\dfrac{52}{3}\right)\sqrt{5}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\dfrac{45}{7}-\left(\left(-\dfrac{11}{6}\right)\sqrt{20}\right)\right)\times\left(\left(\left(\left(7\right)\sqrt{45}\right)-\dfrac{33}{4}+\dfrac{37}{5}\right)-4-\left(\left(0\right)\sqrt{25}\right)\right)\\
&=&\left(\dfrac{45}{7}-\left(\left(-\dfrac{11}{3}\right)\sqrt{5}\right)\right)\times\left(\left(\left(\left(21\right)\sqrt{5}\right)-\dfrac{33}{4}+\dfrac{37}{5}\right)-4-0\right)\\
&=&\left(\dfrac{45}{7}+\left(\dfrac{11}{3}\right)\sqrt{5}\right)\left(\left(21\right)\sqrt{5}-\dfrac{97}{20}\right)\\
&=&\left(\dfrac{7033}{60}\right)\sqrt{5}-\dfrac{873}{28}+\left(77\right)\sqrt{25}\\
&=&\left(\dfrac{7033}{60}\right)\sqrt{5}+\dfrac{9907}{28}\\
\end{eqnarray*}