L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Soit \( X=\left(-\dfrac{61}{8}\right)\sqrt{49}+\left(0\right)\sqrt{49}+\left(-\dfrac{7}{4}\right)\sqrt{28}+\left(-\dfrac{5}{2}\right)\sqrt{49}+\left(\dfrac{44}{3}\right)\sqrt{175}+\left(-1\right)\sqrt{49}-\dfrac{10}{3}+\left(\dfrac{32}{7}\right)\sqrt{28}\) et \( Y=\left(-\dfrac{9}{2}\right)\sqrt{63}\) . 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{61}{8}\right)\sqrt{49}+\left(0\right)\sqrt{49}+\left(-\dfrac{7}{4}\right)\sqrt{28}+\left(-\dfrac{5}{2}\right)\sqrt{49}+\left(\dfrac{44}{3}\right)\sqrt{175}+\left(-1\right)\sqrt{49}-\dfrac{10}{3}+\left(\dfrac{32}{7}\right)\sqrt{28}\right)+\left(\left(-\dfrac{9}{2}\right)\sqrt{63}\right)\\
&=&\left(-\dfrac{427}{8}+0+\left(-\dfrac{7}{2}\right)\sqrt{7}-\dfrac{35}{2}+\left(\dfrac{220}{3}\right)\sqrt{7}-7-\dfrac{10}{3}+\left(\dfrac{64}{7}\right)\sqrt{7}\right)+\left(\left(-\dfrac{27}{2}\right)\sqrt{7}\right)\\
&=&-\dfrac{427}{8}+0+\left(-\dfrac{7}{2}\right)\sqrt{7}-\dfrac{35}{2}+\left(\dfrac{220}{3}\right)\sqrt{7}-7-\dfrac{10}{3}+\left(\dfrac{64}{7}\right)\sqrt{7}+\left(-\dfrac{27}{2}\right)\sqrt{7}\\
&=&-\dfrac{1949}{24}+\left(\dfrac{1375}{21}\right)\sqrt{7}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(-\dfrac{61}{8}\right)\sqrt{49}+\left(0\right)\sqrt{49}+\left(-\dfrac{7}{4}\right)\sqrt{28}+\left(-\dfrac{5}{2}\right)\sqrt{49}+\left(\dfrac{44}{3}\right)\sqrt{175}+\left(-1\right)\sqrt{49}-\dfrac{10}{3}+\left(\dfrac{32}{7}\right)\sqrt{28}\right)-\left(\left(-\dfrac{9}{2}\right)\sqrt{63}\right)\\
&=&\left(-\dfrac{427}{8}+0+\left(-\dfrac{7}{2}\right)\sqrt{7}-\dfrac{35}{2}+\left(\dfrac{220}{3}\right)\sqrt{7}-7-\dfrac{10}{3}+\left(\dfrac{64}{7}\right)\sqrt{7}\right)-\left(\left(-\dfrac{27}{2}\right)\sqrt{7}\right)\\
&=&\left(-\dfrac{1949}{24}+\left(\dfrac{3317}{42}\right)\sqrt{7}\right)-\left(\left(-\dfrac{27}{2}\right)\sqrt{7}\right)\\
&=&-\dfrac{1949}{24}+\left(\dfrac{3317}{42}\right)\sqrt{7}+\left(\dfrac{27}{2}\right)\sqrt{7}\\
&=&-\dfrac{1949}{24}+\left(\dfrac{1942}{21}\right)\sqrt{7}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(-\dfrac{61}{8}\right)\sqrt{49}+\left(0\right)\sqrt{49}+\left(-\dfrac{7}{4}\right)\sqrt{28}+\left(-\dfrac{5}{2}\right)\sqrt{49}+\left(\dfrac{44}{3}\right)\sqrt{175}+\left(-1\right)\sqrt{49}-\dfrac{10}{3}+\left(\dfrac{32}{7}\right)\sqrt{28}\right)\times\left(\left(-\dfrac{9}{2}\right)\sqrt{63}\right)\\
&=&\left(-\dfrac{427}{8}+0+\left(-\dfrac{7}{2}\right)\sqrt{7}-\dfrac{35}{2}+\left(\dfrac{220}{3}\right)\sqrt{7}-7-\dfrac{10}{3}+\left(\dfrac{64}{7}\right)\sqrt{7}\right)\times\left(\left(-\dfrac{27}{2}\right)\sqrt{7}\right)\\
&=&\left(-\dfrac{1949}{24}+\left(\dfrac{3317}{42}\right)\sqrt{7}\right)\left(\left(-\dfrac{27}{2}\right)\sqrt{7}\right)\\
&=&\left(\dfrac{17541}{16}\right)\sqrt{7}+\left(-\dfrac{29853}{28}\right)\sqrt{49}\\
&=&\left(\dfrac{17541}{16}\right)\sqrt{7}-\dfrac{29853}{4}\\
\end{eqnarray*}