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 \( X=-\dfrac{5}{2}+\left(9\right)\sqrt{175}+0-\dfrac{29}{4}\) et \( Y=\left(\left(\dfrac{7}{3}\right)\sqrt{175}\right)-\left(\left(-\dfrac{47}{4}\right)\sqrt{63}\right)-\left(\left(-3\right)\sqrt{175}\right)-\left(\dfrac{79}{3}+\left(\dfrac{62}{5}\right)\sqrt{63}+\left(\dfrac{62}{5}\right)\sqrt{63}\right)\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(-\dfrac{5}{2}+\left(9\right)\sqrt{175}+0-\dfrac{29}{4}\right)+\left(\left(\left(\dfrac{7}{3}\right)\sqrt{175}\right)-\left(\left(-\dfrac{47}{4}\right)\sqrt{63}\right)-\left(\left(-3\right)\sqrt{175}\right)-\left(\dfrac{79}{3}+\left(\dfrac{62}{5}\right)\sqrt{63}+\left(\dfrac{62}{5}\right)\sqrt{63}\right)\right)\\
&=&\left(-\dfrac{5}{2}+\left(45\right)\sqrt{7}+0-\dfrac{29}{4}\right)+\left(\left(\left(\dfrac{35}{3}\right)\sqrt{7}\right)-\left(\left(-\dfrac{141}{4}\right)\sqrt{7}\right)-\left(\left(-15\right)\sqrt{7}\right)-\left(\dfrac{79}{3}+\left(\dfrac{186}{5}\right)\sqrt{7}+\left(\dfrac{186}{5}\right)\sqrt{7}\right)\right)\\
&=&-\dfrac{5}{2}+\left(45\right)\sqrt{7}+0-\dfrac{29}{4}+\left(\left(\dfrac{35}{3}\right)\sqrt{7}\right)-\left(\left(-\dfrac{141}{4}\right)\sqrt{7}\right)-\left(\left(-15\right)\sqrt{7}\right)-\left(\dfrac{79}{3}+\left(\dfrac{186}{5}\right)\sqrt{7}+\left(\dfrac{186}{5}\right)\sqrt{7}\right)\\
&=&-\dfrac{433}{12}+\left(\dfrac{1951}{60}\right)\sqrt{7}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(-\dfrac{5}{2}+\left(9\right)\sqrt{175}+0-\dfrac{29}{4}\right)-\left(\left(\left(\dfrac{7}{3}\right)\sqrt{175}\right)-\left(\left(-\dfrac{47}{4}\right)\sqrt{63}\right)-\left(\left(-3\right)\sqrt{175}\right)-\left(\dfrac{79}{3}+\left(\dfrac{62}{5}\right)\sqrt{63}+\left(\dfrac{62}{5}\right)\sqrt{63}\right)\right)\\
&=&\left(-\dfrac{5}{2}+\left(45\right)\sqrt{7}+0-\dfrac{29}{4}\right)-\left(\left(\left(\dfrac{35}{3}\right)\sqrt{7}\right)-\left(\left(-\dfrac{141}{4}\right)\sqrt{7}\right)-\left(\left(-15\right)\sqrt{7}\right)-\left(\dfrac{79}{3}+\left(\dfrac{186}{5}\right)\sqrt{7}+\left(\dfrac{186}{5}\right)\sqrt{7}\right)\right)\\
&=&\left(-\dfrac{39}{4}+\left(45\right)\sqrt{7}\right)-\left(\left(-\dfrac{749}{60}\right)\sqrt{7}-\dfrac{79}{3}\right)\\
&=&-\dfrac{39}{4}+\left(45\right)\sqrt{7}+\left(\dfrac{749}{60}\right)\sqrt{7}+\dfrac{79}{3}\\
&=&\dfrac{199}{12}+\left(\dfrac{3449}{60}\right)\sqrt{7}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(-\dfrac{5}{2}+\left(9\right)\sqrt{175}+0-\dfrac{29}{4}\right)\times\left(\left(\left(\dfrac{7}{3}\right)\sqrt{175}\right)-\left(\left(-\dfrac{47}{4}\right)\sqrt{63}\right)-\left(\left(-3\right)\sqrt{175}\right)-\left(\dfrac{79}{3}+\left(\dfrac{62}{5}\right)\sqrt{63}+\left(\dfrac{62}{5}\right)\sqrt{63}\right)\right)\\
&=&\left(-\dfrac{5}{2}+\left(45\right)\sqrt{7}+0-\dfrac{29}{4}\right)\times\left(\left(\left(\dfrac{35}{3}\right)\sqrt{7}\right)-\left(\left(-\dfrac{141}{4}\right)\sqrt{7}\right)-\left(\left(-15\right)\sqrt{7}\right)-\left(\dfrac{79}{3}+\left(\dfrac{186}{5}\right)\sqrt{7}+\left(\dfrac{186}{5}\right)\sqrt{7}\right)\right)\\
&=&\left(-\dfrac{39}{4}+\left(45\right)\sqrt{7}\right)\left(\left(-\dfrac{749}{60}\right)\sqrt{7}-\dfrac{79}{3}\right)\\
&=&\left(-\dfrac{85063}{80}\right)\sqrt{7}+\dfrac{1027}{4}+\left(-\dfrac{2247}{4}\right)\sqrt{49}\\
&=&\left(-\dfrac{85063}{80}\right)\sqrt{7}-\dfrac{7351}{2}\\
\end{eqnarray*}