L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Soit \( X=\left(-\dfrac{21}{5}\right)\sqrt{9}\) et \( Y=\left(\left(-6\right)\sqrt{9}\right)-\left(\left(\left(-\dfrac{5}{2}\right)\sqrt{75}\right)-\left(\left(-\dfrac{8}{3}\right)\sqrt{27}\right)-\left(\left(-8\right)\sqrt{9}\right)-\dfrac{34}{5}\right)+\dfrac{45}{2}\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(\left(-\dfrac{21}{5}\right)\sqrt{9}\right)+\left(\left(\left(-6\right)\sqrt{9}\right)-\left(\left(\left(-\dfrac{5}{2}\right)\sqrt{75}\right)-\left(\left(-\dfrac{8}{3}\right)\sqrt{27}\right)-\left(\left(-8\right)\sqrt{9}\right)-\dfrac{34}{5}\right)+\dfrac{45}{2}\right)\\
&=&\left(-\dfrac{63}{5}\right)+\left(-18-\left(\left(\left(-\dfrac{25}{2}\right)\sqrt{3}\right)-\left(\left(-8\right)\sqrt{3}\right)+24-\dfrac{34}{5}\right)+\dfrac{45}{2}\right)\\
&=&-\dfrac{63}{5}-18-\left(\left(\left(-\dfrac{25}{2}\right)\sqrt{3}\right)-\left(\left(-8\right)\sqrt{3}\right)+24-\dfrac{34}{5}\right)+\dfrac{45}{2}\\
&=&-\dfrac{253}{10}+\left(\dfrac{9}{2}\right)\sqrt{3}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(-\dfrac{21}{5}\right)\sqrt{9}\right)-\left(\left(\left(-6\right)\sqrt{9}\right)-\left(\left(\left(-\dfrac{5}{2}\right)\sqrt{75}\right)-\left(\left(-\dfrac{8}{3}\right)\sqrt{27}\right)-\left(\left(-8\right)\sqrt{9}\right)-\dfrac{34}{5}\right)+\dfrac{45}{2}\right)\\
&=&\left(-\dfrac{63}{5}\right)-\left(-18-\left(\left(\left(-\dfrac{25}{2}\right)\sqrt{3}\right)-\left(\left(-8\right)\sqrt{3}\right)+24-\dfrac{34}{5}\right)+\dfrac{45}{2}\right)\\
&=&\left(-\dfrac{63}{5}\right)-\left(-\dfrac{127}{10}+\left(\dfrac{9}{2}\right)\sqrt{3}\right)\\
&=&-\dfrac{63}{5}+\dfrac{127}{10}+\left(-\dfrac{9}{2}\right)\sqrt{3}\\
&=&\dfrac{1}{10}+\left(-\dfrac{9}{2}\right)\sqrt{3}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(-\dfrac{21}{5}\right)\sqrt{9}\right)\times\left(\left(\left(-6\right)\sqrt{9}\right)-\left(\left(\left(-\dfrac{5}{2}\right)\sqrt{75}\right)-\left(\left(-\dfrac{8}{3}\right)\sqrt{27}\right)-\left(\left(-8\right)\sqrt{9}\right)-\dfrac{34}{5}\right)+\dfrac{45}{2}\right)\\
&=&\left(-\dfrac{63}{5}\right)\times\left(-18-\left(\left(\left(-\dfrac{25}{2}\right)\sqrt{3}\right)-\left(\left(-8\right)\sqrt{3}\right)+24-\dfrac{34}{5}\right)+\dfrac{45}{2}\right)\\
&=&\left(-\dfrac{63}{5}\right)\left(-\dfrac{127}{10}+\left(\dfrac{9}{2}\right)\sqrt{3}\right)\\
&=&\dfrac{8001}{50}+\left(-\dfrac{567}{10}\right)\sqrt{3}\\
&=&\dfrac{8001}{50}+\left(-\dfrac{567}{10}\right)\sqrt{3}\\
\end{eqnarray*}