L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Soit \( X=\left(\left(-\dfrac{68}{5}\right)\sqrt{125}\right)-\left(\left(\dfrac{47}{2}\right)\sqrt{25}\right)+\left(-\dfrac{29}{6}\right)\sqrt{125}\) et \( Y=8-\left(\left(\left(-\dfrac{10}{3}\right)\sqrt{25}\right)-\left(\left(-\dfrac{56}{5}\right)\sqrt{25}\right)\right)\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(\left(\left(-\dfrac{68}{5}\right)\sqrt{125}\right)-\left(\left(\dfrac{47}{2}\right)\sqrt{25}\right)+\left(-\dfrac{29}{6}\right)\sqrt{125}\right)+\left(8-\left(\left(\left(-\dfrac{10}{3}\right)\sqrt{25}\right)-\left(\left(-\dfrac{56}{5}\right)\sqrt{25}\right)\right)\right)\\
&=&\left(\left(\left(-68\right)\sqrt{5}\right)-\dfrac{235}{2}+\left(-\dfrac{145}{6}\right)\sqrt{5}\right)+\left(8-\left(-\dfrac{50}{3}+56\right)\right)\\
&=&\left(\left(-68\right)\sqrt{5}\right)-\dfrac{235}{2}+\left(-\dfrac{145}{6}\right)\sqrt{5}+8-\left(-\dfrac{50}{3}+56\right)\\
&=&\left(-\dfrac{553}{6}\right)\sqrt{5}-\dfrac{893}{6}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\left(-\dfrac{68}{5}\right)\sqrt{125}\right)-\left(\left(\dfrac{47}{2}\right)\sqrt{25}\right)+\left(-\dfrac{29}{6}\right)\sqrt{125}\right)-\left(8-\left(\left(\left(-\dfrac{10}{3}\right)\sqrt{25}\right)-\left(\left(-\dfrac{56}{5}\right)\sqrt{25}\right)\right)\right)\\
&=&\left(\left(\left(-68\right)\sqrt{5}\right)-\dfrac{235}{2}+\left(-\dfrac{145}{6}\right)\sqrt{5}\right)-\left(8-\left(-\dfrac{50}{3}+56\right)\right)\\
&=&\left(\left(-\dfrac{553}{6}\right)\sqrt{5}-\dfrac{235}{2}\right)-\left(-\dfrac{94}{3}\right)\\
&=&\left(-\dfrac{553}{6}\right)\sqrt{5}-\dfrac{235}{2}+\dfrac{94}{3}\\
&=&\left(-\dfrac{553}{6}\right)\sqrt{5}-\dfrac{517}{6}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\left(-\dfrac{68}{5}\right)\sqrt{125}\right)-\left(\left(\dfrac{47}{2}\right)\sqrt{25}\right)+\left(-\dfrac{29}{6}\right)\sqrt{125}\right)\times\left(8-\left(\left(\left(-\dfrac{10}{3}\right)\sqrt{25}\right)-\left(\left(-\dfrac{56}{5}\right)\sqrt{25}\right)\right)\right)\\
&=&\left(\left(\left(-68\right)\sqrt{5}\right)-\dfrac{235}{2}+\left(-\dfrac{145}{6}\right)\sqrt{5}\right)\times\left(8-\left(-\dfrac{50}{3}+56\right)\right)\\
&=&\left(\left(-\dfrac{553}{6}\right)\sqrt{5}-\dfrac{235}{2}\right)\left(-\dfrac{94}{3}\right)\\
&=&\left(\dfrac{25991}{9}\right)\sqrt{5}+\dfrac{11045}{3}\\
&=&\left(\dfrac{25991}{9}\right)\sqrt{5}+\dfrac{11045}{3}\\
\end{eqnarray*}