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 \( X=\left(4\right)\sqrt{20}\) et \( Y=\left(\left(-\dfrac{69}{5}\right)\sqrt{20}\right)-\left(\left(-\dfrac{9}{5}\right)\sqrt{125}\right)-\left(\left(2\right)\sqrt{45}\right)+\left(\left(\dfrac{6}{7}\right)\sqrt{25}\right)-\left(\left(-9\right)\sqrt{45}\right)-\left(\left(\dfrac{7}{2}\right)\sqrt{20}\right)+1-\dfrac{69}{4}-\left(\left(-\dfrac{21}{2}\right)\sqrt{20}\right)-\left(\left(\dfrac{1}{6}\right)\sqrt{20}\right)\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(\left(4\right)\sqrt{20}\right)+\left(\left(\left(-\dfrac{69}{5}\right)\sqrt{20}\right)-\left(\left(-\dfrac{9}{5}\right)\sqrt{125}\right)-\left(\left(2\right)\sqrt{45}\right)+\left(\left(\dfrac{6}{7}\right)\sqrt{25}\right)-\left(\left(-9\right)\sqrt{45}\right)-\left(\left(\dfrac{7}{2}\right)\sqrt{20}\right)+1-\dfrac{69}{4}-\left(\left(-\dfrac{21}{2}\right)\sqrt{20}\right)-\left(\left(\dfrac{1}{6}\right)\sqrt{20}\right)\right)\\
&=&\left(\left(8\right)\sqrt{5}\right)+\left(\left(\left(-\dfrac{138}{5}\right)\sqrt{5}\right)-\left(\left(-9\right)\sqrt{5}\right)-\left(\left(6\right)\sqrt{5}\right)+\dfrac{30}{7}-\left(\left(-27\right)\sqrt{5}\right)-\left(\left(7\right)\sqrt{5}\right)+1-\dfrac{69}{4}-\left(\left(-21\right)\sqrt{5}\right)-\left(\left(\dfrac{1}{3}\right)\sqrt{5}\right)\right)\\
&=&\left(8\right)\sqrt{5}+\left(\left(-\dfrac{138}{5}\right)\sqrt{5}\right)-\left(\left(-9\right)\sqrt{5}\right)-\left(\left(6\right)\sqrt{5}\right)+\dfrac{30}{7}-\left(\left(-27\right)\sqrt{5}\right)-\left(\left(7\right)\sqrt{5}\right)+1-\dfrac{69}{4}-\left(\left(-21\right)\sqrt{5}\right)-\left(\left(\dfrac{1}{3}\right)\sqrt{5}\right)\\
&=&\left(\dfrac{361}{15}\right)\sqrt{5}-\dfrac{335}{28}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(4\right)\sqrt{20}\right)-\left(\left(\left(-\dfrac{69}{5}\right)\sqrt{20}\right)-\left(\left(-\dfrac{9}{5}\right)\sqrt{125}\right)-\left(\left(2\right)\sqrt{45}\right)+\left(\left(\dfrac{6}{7}\right)\sqrt{25}\right)-\left(\left(-9\right)\sqrt{45}\right)-\left(\left(\dfrac{7}{2}\right)\sqrt{20}\right)+1-\dfrac{69}{4}-\left(\left(-\dfrac{21}{2}\right)\sqrt{20}\right)-\left(\left(\dfrac{1}{6}\right)\sqrt{20}\right)\right)\\
&=&\left(\left(8\right)\sqrt{5}\right)-\left(\left(\left(-\dfrac{138}{5}\right)\sqrt{5}\right)-\left(\left(-9\right)\sqrt{5}\right)-\left(\left(6\right)\sqrt{5}\right)+\dfrac{30}{7}-\left(\left(-27\right)\sqrt{5}\right)-\left(\left(7\right)\sqrt{5}\right)+1-\dfrac{69}{4}-\left(\left(-21\right)\sqrt{5}\right)-\left(\left(\dfrac{1}{3}\right)\sqrt{5}\right)\right)\\
&=&\left(\left(8\right)\sqrt{5}\right)-\left(\left(\dfrac{241}{15}\right)\sqrt{5}-\dfrac{335}{28}\right)\\
&=&\left(8\right)\sqrt{5}+\left(-\dfrac{241}{15}\right)\sqrt{5}+\dfrac{335}{28}\\
&=&\left(-\dfrac{121}{15}\right)\sqrt{5}+\dfrac{335}{28}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(4\right)\sqrt{20}\right)\times\left(\left(\left(-\dfrac{69}{5}\right)\sqrt{20}\right)-\left(\left(-\dfrac{9}{5}\right)\sqrt{125}\right)-\left(\left(2\right)\sqrt{45}\right)+\left(\left(\dfrac{6}{7}\right)\sqrt{25}\right)-\left(\left(-9\right)\sqrt{45}\right)-\left(\left(\dfrac{7}{2}\right)\sqrt{20}\right)+1-\dfrac{69}{4}-\left(\left(-\dfrac{21}{2}\right)\sqrt{20}\right)-\left(\left(\dfrac{1}{6}\right)\sqrt{20}\right)\right)\\
&=&\left(\left(8\right)\sqrt{5}\right)\times\left(\left(\left(-\dfrac{138}{5}\right)\sqrt{5}\right)-\left(\left(-9\right)\sqrt{5}\right)-\left(\left(6\right)\sqrt{5}\right)+\dfrac{30}{7}-\left(\left(-27\right)\sqrt{5}\right)-\left(\left(7\right)\sqrt{5}\right)+1-\dfrac{69}{4}-\left(\left(-21\right)\sqrt{5}\right)-\left(\left(\dfrac{1}{3}\right)\sqrt{5}\right)\right)\\
&=&\left(\left(8\right)\sqrt{5}\right)\left(\left(\dfrac{241}{15}\right)\sqrt{5}-\dfrac{335}{28}\right)\\
&=&\left(\dfrac{1928}{15}\right)\sqrt{25}+\left(-\dfrac{670}{7}\right)\sqrt{5}\\
&=&\dfrac{1928}{3}+\left(-\dfrac{670}{7}\right)\sqrt{5}\\
\end{eqnarray*}