L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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Exercice
Soit \( X=2+\left(4\right)\sqrt{49}+\left(\dfrac{9}{2}\right)\sqrt{49}\) et \( Y=\left(\left(-\dfrac{81}{4}\right)\sqrt{28}\right)-\left(\left(\left(-5\right)\sqrt{175}\right)-\left(\left(-\dfrac{17}{3}\right)\sqrt{28}\right)+\dfrac{62}{5}-\left(\left(-\dfrac{66}{7}\right)\sqrt{49}\right)-\left(\left(8\right)\sqrt{175}\right)\right)-\left(\left(\left(-\dfrac{49}{9}\right)\sqrt{28}\right)-\dfrac{32}{3}\right)-\left(\left(\dfrac{12}{7}\right)\sqrt{28}+\left(-4\right)\sqrt{63}+\left(\dfrac{17}{6}\right)\sqrt{49}+\left(-\dfrac{7}{2}\right)\sqrt{49}\right)-\left(\left(\left(-\dfrac{17}{3}\right)\sqrt{28}\right)-\left(\left(-8\right)\sqrt{63}\right)-\left(\left(2\right)\sqrt{63}\right)\right)\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(2+\left(4\right)\sqrt{49}+\left(\dfrac{9}{2}\right)\sqrt{49}\right)+\left(\left(\left(-\dfrac{81}{4}\right)\sqrt{28}\right)-\left(\left(\left(-5\right)\sqrt{175}\right)-\left(\left(-\dfrac{17}{3}\right)\sqrt{28}\right)+\dfrac{62}{5}-\left(\left(-\dfrac{66}{7}\right)\sqrt{49}\right)-\left(\left(8\right)\sqrt{175}\right)\right)-\left(\left(\left(-\dfrac{49}{9}\right)\sqrt{28}\right)-\dfrac{32}{3}\right)-\left(\left(\dfrac{12}{7}\right)\sqrt{28}+\left(-4\right)\sqrt{63}+\left(\dfrac{17}{6}\right)\sqrt{49}+\left(-\dfrac{7}{2}\right)\sqrt{49}\right)-\left(\left(\left(-\dfrac{17}{3}\right)\sqrt{28}\right)-\left(\left(-8\right)\sqrt{63}\right)-\left(\left(2\right)\sqrt{63}\right)\right)\right)\\
&=&\left(2+28+\dfrac{63}{2}\right)+\left(\left(\left(-\dfrac{81}{2}\right)\sqrt{7}\right)-\left(\left(\left(-25\right)\sqrt{7}\right)-\left(\left(-\dfrac{34}{3}\right)\sqrt{7}\right)+\dfrac{62}{5}+66-\left(\left(40\right)\sqrt{7}\right)\right)-\left(\left(\left(-\dfrac{98}{9}\right)\sqrt{7}\right)-\dfrac{32}{3}\right)-\left(\left(\dfrac{24}{7}\right)\sqrt{7}+\left(-12\right)\sqrt{7}+\dfrac{119}{6}-\dfrac{49}{2}\right)-\left(\left(\left(-\dfrac{34}{3}\right)\sqrt{7}\right)-\left(\left(-24\right)\sqrt{7}\right)-\left(\left(6\right)\sqrt{7}\right)\right)\right)\\
&=&2+28+\dfrac{63}{2}+\left(\left(-\dfrac{81}{2}\right)\sqrt{7}\right)-\left(\left(\left(-25\right)\sqrt{7}\right)-\left(\left(-\dfrac{34}{3}\right)\sqrt{7}\right)+\dfrac{62}{5}+66-\left(\left(40\right)\sqrt{7}\right)\right)-\left(\left(\left(-\dfrac{98}{9}\right)\sqrt{7}\right)-\dfrac{32}{3}\right)-\left(\left(\dfrac{24}{7}\right)\sqrt{7}+\left(-12\right)\sqrt{7}+\dfrac{119}{6}-\dfrac{49}{2}\right)-\left(\left(\left(-\dfrac{34}{3}\right)\sqrt{7}\right)-\left(\left(-24\right)\sqrt{7}\right)-\left(\left(6\right)\sqrt{7}\right)\right)\\
&=&-\dfrac{47}{30}+\left(\dfrac{3271}{126}\right)\sqrt{7}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(2+\left(4\right)\sqrt{49}+\left(\dfrac{9}{2}\right)\sqrt{49}\right)-\left(\left(\left(-\dfrac{81}{4}\right)\sqrt{28}\right)-\left(\left(\left(-5\right)\sqrt{175}\right)-\left(\left(-\dfrac{17}{3}\right)\sqrt{28}\right)+\dfrac{62}{5}-\left(\left(-\dfrac{66}{7}\right)\sqrt{49}\right)-\left(\left(8\right)\sqrt{175}\right)\right)-\left(\left(\left(-\dfrac{49}{9}\right)\sqrt{28}\right)-\dfrac{32}{3}\right)-\left(\left(\dfrac{12}{7}\right)\sqrt{28}+\left(-4\right)\sqrt{63}+\left(\dfrac{17}{6}\right)\sqrt{49}+\left(-\dfrac{7}{2}\right)\sqrt{49}\right)-\left(\left(\left(-\dfrac{17}{3}\right)\sqrt{28}\right)-\left(\left(-8\right)\sqrt{63}\right)-\left(\left(2\right)\sqrt{63}\right)\right)\right)\\
&=&\left(2+28+\dfrac{63}{2}\right)-\left(\left(\left(-\dfrac{81}{2}\right)\sqrt{7}\right)-\left(\left(\left(-25\right)\sqrt{7}\right)-\left(\left(-\dfrac{34}{3}\right)\sqrt{7}\right)+\dfrac{62}{5}+66-\left(\left(40\right)\sqrt{7}\right)\right)-\left(\left(\left(-\dfrac{98}{9}\right)\sqrt{7}\right)-\dfrac{32}{3}\right)-\left(\left(\dfrac{24}{7}\right)\sqrt{7}+\left(-12\right)\sqrt{7}+\dfrac{119}{6}-\dfrac{49}{2}\right)-\left(\left(\left(-\dfrac{34}{3}\right)\sqrt{7}\right)-\left(\left(-24\right)\sqrt{7}\right)-\left(\left(6\right)\sqrt{7}\right)\right)\right)\\
&=&\left(\dfrac{123}{2}\right)-\left(\left(\dfrac{3271}{126}\right)\sqrt{7}-\dfrac{946}{15}\right)\\
&=&\dfrac{123}{2}+\left(-\dfrac{3271}{126}\right)\sqrt{7}+\dfrac{946}{15}\\
&=&\dfrac{3737}{30}+\left(-\dfrac{3271}{126}\right)\sqrt{7}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(2+\left(4\right)\sqrt{49}+\left(\dfrac{9}{2}\right)\sqrt{49}\right)\times\left(\left(\left(-\dfrac{81}{4}\right)\sqrt{28}\right)-\left(\left(\left(-5\right)\sqrt{175}\right)-\left(\left(-\dfrac{17}{3}\right)\sqrt{28}\right)+\dfrac{62}{5}-\left(\left(-\dfrac{66}{7}\right)\sqrt{49}\right)-\left(\left(8\right)\sqrt{175}\right)\right)-\left(\left(\left(-\dfrac{49}{9}\right)\sqrt{28}\right)-\dfrac{32}{3}\right)-\left(\left(\dfrac{12}{7}\right)\sqrt{28}+\left(-4\right)\sqrt{63}+\left(\dfrac{17}{6}\right)\sqrt{49}+\left(-\dfrac{7}{2}\right)\sqrt{49}\right)-\left(\left(\left(-\dfrac{17}{3}\right)\sqrt{28}\right)-\left(\left(-8\right)\sqrt{63}\right)-\left(\left(2\right)\sqrt{63}\right)\right)\right)\\
&=&\left(2+28+\dfrac{63}{2}\right)\times\left(\left(\left(-\dfrac{81}{2}\right)\sqrt{7}\right)-\left(\left(\left(-25\right)\sqrt{7}\right)-\left(\left(-\dfrac{34}{3}\right)\sqrt{7}\right)+\dfrac{62}{5}+66-\left(\left(40\right)\sqrt{7}\right)\right)-\left(\left(\left(-\dfrac{98}{9}\right)\sqrt{7}\right)-\dfrac{32}{3}\right)-\left(\left(\dfrac{24}{7}\right)\sqrt{7}+\left(-12\right)\sqrt{7}+\dfrac{119}{6}-\dfrac{49}{2}\right)-\left(\left(\left(-\dfrac{34}{3}\right)\sqrt{7}\right)-\left(\left(-24\right)\sqrt{7}\right)-\left(\left(6\right)\sqrt{7}\right)\right)\right)\\
&=&\left(\dfrac{123}{2}\right)\left(\left(\dfrac{3271}{126}\right)\sqrt{7}-\dfrac{946}{15}\right)\\
&=&\left(\dfrac{134111}{84}\right)\sqrt{7}-\dfrac{19393}{5}\\
&=&\left(\dfrac{134111}{84}\right)\sqrt{7}-\dfrac{19393}{5}\\
\end{eqnarray*}