L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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Exercice
Soit \( X=\left(-\dfrac{13}{2}-\left(\left(\dfrac{33}{2}\right)\sqrt{25}\right)-\left(\left(0\right)\sqrt{45}\right)\right)-\left(\left(-\dfrac{5}{8}\right)\sqrt{45}+\left(-9\right)\sqrt{25}\right)-\left(\left(\dfrac{20}{7}\right)\sqrt{20}+\left(-\dfrac{34}{9}\right)\sqrt{25}+\left(-\dfrac{48}{5}\right)\sqrt{125}\right)\) et \( Y=\left(-8-\left(\left(\dfrac{26}{3}\right)\sqrt{45}\right)\right)-\left(-\dfrac{67}{5}+\left(-\dfrac{6}{5}\right)\sqrt{20}+\left(7\right)\sqrt{20}\right)\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(\left(-\dfrac{13}{2}-\left(\left(\dfrac{33}{2}\right)\sqrt{25}\right)-\left(\left(0\right)\sqrt{45}\right)\right)-\left(\left(-\dfrac{5}{8}\right)\sqrt{45}+\left(-9\right)\sqrt{25}\right)-\left(\left(\dfrac{20}{7}\right)\sqrt{20}+\left(-\dfrac{34}{9}\right)\sqrt{25}+\left(-\dfrac{48}{5}\right)\sqrt{125}\right)\right)+\left(\left(-8-\left(\left(\dfrac{26}{3}\right)\sqrt{45}\right)\right)-\left(-\dfrac{67}{5}+\left(-\dfrac{6}{5}\right)\sqrt{20}+\left(7\right)\sqrt{20}\right)\right)\\
&=&\left(\left(-\dfrac{13}{2}-\dfrac{165}{2}-\left(\left(0\right)\sqrt{5}\right)\right)-\left(\left(-\dfrac{15}{8}\right)\sqrt{5}-45\right)-\left(\left(\dfrac{40}{7}\right)\sqrt{5}-\dfrac{170}{9}+\left(-48\right)\sqrt{5}\right)\right)+\left(\left(-8-\left(\left(26\right)\sqrt{5}\right)\right)-\left(-\dfrac{67}{5}+\left(-\dfrac{12}{5}\right)\sqrt{5}+\left(14\right)\sqrt{5}\right)\right)\\
&=&\left(-\dfrac{13}{2}-\dfrac{165}{2}-\left(\left(0\right)\sqrt{5}\right)\right)-\left(\left(-\dfrac{15}{8}\right)\sqrt{5}-45\right)-\left(\left(\dfrac{40}{7}\right)\sqrt{5}-\dfrac{170}{9}+\left(-48\right)\sqrt{5}\right)+\left(-8-\left(\left(26\right)\sqrt{5}\right)\right)-\left(-\dfrac{67}{5}+\left(-\dfrac{12}{5}\right)\sqrt{5}+\left(14\right)\sqrt{5}\right)\\
&=&-\dfrac{887}{45}+\left(\dfrac{1837}{280}\right)\sqrt{5}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(-\dfrac{13}{2}-\left(\left(\dfrac{33}{2}\right)\sqrt{25}\right)-\left(\left(0\right)\sqrt{45}\right)\right)-\left(\left(-\dfrac{5}{8}\right)\sqrt{45}+\left(-9\right)\sqrt{25}\right)-\left(\left(\dfrac{20}{7}\right)\sqrt{20}+\left(-\dfrac{34}{9}\right)\sqrt{25}+\left(-\dfrac{48}{5}\right)\sqrt{125}\right)\right)-\left(\left(-8-\left(\left(\dfrac{26}{3}\right)\sqrt{45}\right)\right)-\left(-\dfrac{67}{5}+\left(-\dfrac{6}{5}\right)\sqrt{20}+\left(7\right)\sqrt{20}\right)\right)\\
&=&\left(\left(-\dfrac{13}{2}-\dfrac{165}{2}-\left(\left(0\right)\sqrt{5}\right)\right)-\left(\left(-\dfrac{15}{8}\right)\sqrt{5}-45\right)-\left(\left(\dfrac{40}{7}\right)\sqrt{5}-\dfrac{170}{9}+\left(-48\right)\sqrt{5}\right)\right)-\left(\left(-8-\left(\left(26\right)\sqrt{5}\right)\right)-\left(-\dfrac{67}{5}+\left(-\dfrac{12}{5}\right)\sqrt{5}+\left(14\right)\sqrt{5}\right)\right)\\
&=&\left(-\dfrac{226}{9}+\left(\dfrac{2473}{56}\right)\sqrt{5}\right)-\left(\dfrac{27}{5}+\left(-\dfrac{188}{5}\right)\sqrt{5}\right)\\
&=&-\dfrac{226}{9}+\left(\dfrac{2473}{56}\right)\sqrt{5}+-\dfrac{27}{5}+\left(\dfrac{188}{5}\right)\sqrt{5}\\
&=&-\dfrac{1373}{45}+\left(\dfrac{22893}{280}\right)\sqrt{5}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(-\dfrac{13}{2}-\left(\left(\dfrac{33}{2}\right)\sqrt{25}\right)-\left(\left(0\right)\sqrt{45}\right)\right)-\left(\left(-\dfrac{5}{8}\right)\sqrt{45}+\left(-9\right)\sqrt{25}\right)-\left(\left(\dfrac{20}{7}\right)\sqrt{20}+\left(-\dfrac{34}{9}\right)\sqrt{25}+\left(-\dfrac{48}{5}\right)\sqrt{125}\right)\right)\times\left(\left(-8-\left(\left(\dfrac{26}{3}\right)\sqrt{45}\right)\right)-\left(-\dfrac{67}{5}+\left(-\dfrac{6}{5}\right)\sqrt{20}+\left(7\right)\sqrt{20}\right)\right)\\
&=&\left(\left(-\dfrac{13}{2}-\dfrac{165}{2}-\left(\left(0\right)\sqrt{5}\right)\right)-\left(\left(-\dfrac{15}{8}\right)\sqrt{5}-45\right)-\left(\left(\dfrac{40}{7}\right)\sqrt{5}-\dfrac{170}{9}+\left(-48\right)\sqrt{5}\right)\right)\times\left(\left(-8-\left(\left(26\right)\sqrt{5}\right)\right)-\left(-\dfrac{67}{5}+\left(-\dfrac{12}{5}\right)\sqrt{5}+\left(14\right)\sqrt{5}\right)\right)\\
&=&\left(-\dfrac{226}{9}+\left(\dfrac{2473}{56}\right)\sqrt{5}\right)\left(\dfrac{27}{5}+\left(-\dfrac{188}{5}\right)\sqrt{5}\right)\\
&=&-\dfrac{678}{5}+\left(\dfrac{2980267}{2520}\right)\sqrt{5}+\left(-\dfrac{116231}{70}\right)\sqrt{25}\\
&=&-\dfrac{590647}{70}+\left(\dfrac{2980267}{2520}\right)\sqrt{5}\\
\end{eqnarray*}