Ataraxy

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Exercice

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=\left(8-\left(\left(-\dfrac{63}{4}\right)\sqrt{175}\right)-\left(\left(0\right)\sqrt{175}\right)-\left(\left(\dfrac{39}{4}\right)\sqrt{175}\right)-\left(\left(\dfrac{53}{2}\right)\sqrt{28}\right)\right)-\left(-\dfrac{57}{7}-\left(\left(-2\right)\sqrt{28}\right)-\left(\left(-8\right)\sqrt{49}\right)\right)-\left(\left(-\dfrac{19}{2}\right)\sqrt{49}\right)-\left(\left(-\dfrac{26}{3}\right)\sqrt{28}+\left(\dfrac{37}{5}\right)\sqrt{63}+\left(\dfrac{39}{4}\right)\sqrt{175}+\left(\dfrac{53}{4}\right)\sqrt{175}\right)-\left(\left(9\right)\sqrt{63}+\left(-\dfrac{26}{3}\right)\sqrt{28}+\left(7\right)\sqrt{28}+\dfrac{50}{9}\right)$ et $ Y=\left(\left(\dfrac{35}{4}\right)\sqrt{49}\right)-\left(\left(\dfrac{67}{4}\right)\sqrt{63}\right)-\left(\left(\left(-\dfrac{47}{7}\right)\sqrt{28}\right)-\dfrac{40}{3}-\left(\left(\dfrac{64}{5}\right)\sqrt{49}\right)-\left(\left(\dfrac{31}{9}\right)\sqrt{49}\right)\right)-\left(\left(\left(-3\right)\sqrt{175}\right)-\dfrac{43}{5}\right)-\left(\left(\left(\dfrac{64}{5}\right)\sqrt{49}\right)-\left(\left(-\dfrac{55}{7}\right)\sqrt{49}\right)-\left(\left(-\dfrac{2}{3}\right)\sqrt{175}\right)-\left(\left(\dfrac{11}{6}\right)\sqrt{63}\right)-\left(\left(\dfrac{33}{5}\right)\sqrt{175}\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(8-\left(\left(-\dfrac{63}{4}\right)\sqrt{175}\right)-\left(\left(0\right)\sqrt{175}\right)-\left(\left(\dfrac{39}{4}\right)\sqrt{175}\right)-\left(\left(\dfrac{53}{2}\right)\sqrt{28}\right)\right)-\left(-\dfrac{57}{7}-\left(\left(-2\right)\sqrt{28}\right)-\left(\left(-8\right)\sqrt{49}\right)\right)-\left(\left(-\dfrac{19}{2}\right)\sqrt{49}\right)-\left(\left(-\dfrac{26}{3}\right)\sqrt{28}+\left(\dfrac{37}{5}\right)\sqrt{63}+\left(\dfrac{39}{4}\right)\sqrt{175}+\left(\dfrac{53}{4}\right)\sqrt{175}\right)-\left(\left(9\right)\sqrt{63}+\left(-\dfrac{26}{3}\right)\sqrt{28}+\left(7\right)\sqrt{28}+\dfrac{50}{9}\right)\right)+\left(\left(\left(\dfrac{35}{4}\right)\sqrt{49}\right)-\left(\left(\dfrac{67}{4}\right)\sqrt{63}\right)-\left(\left(\left(-\dfrac{47}{7}\right)\sqrt{28}\right)-\dfrac{40}{3}-\left(\left(\dfrac{64}{5}\right)\sqrt{49}\right)-\left(\left(\dfrac{31}{9}\right)\sqrt{49}\right)\right)-\left(\left(\left(-3\right)\sqrt{175}\right)-\dfrac{43}{5}\right)-\left(\left(\left(\dfrac{64}{5}\right)\sqrt{49}\right)-\left(\left(-\dfrac{55}{7}\right)\sqrt{49}\right)-\left(\left(-\dfrac{2}{3}\right)\sqrt{175}\right)-\left(\left(\dfrac{11}{6}\right)\sqrt{63}\right)-\left(\left(\dfrac{33}{5}\right)\sqrt{175}\right)\right)\right)\\ &=&\left(\left(8-\left(\left(-\dfrac{315}{4}\right)\sqrt{7}\right)-\left(\left(0\right)\sqrt{7}\right)-\left(\left(\dfrac{195}{4}\right)\sqrt{7}\right)-\left(\left(53\right)\sqrt{7}\right)\right)-\left(-\dfrac{57}{7}-\left(\left(-4\right)\sqrt{7}\right)+56\right)+\dfrac{133}{2}-\left(\left(-\dfrac{52}{3}\right)\sqrt{7}+\left(\dfrac{111}{5}\right)\sqrt{7}+\left(\dfrac{195}{4}\right)\sqrt{7}+\left(\dfrac{265}{4}\right)\sqrt{7}\right)-\left(\left(27\right)\sqrt{7}+\left(-\dfrac{52}{3}\right)\sqrt{7}+\left(14\right)\sqrt{7}+\dfrac{50}{9}\right)\right)+\left(\dfrac{245}{4}-\left(\left(\dfrac{201}{4}\right)\sqrt{7}\right)-\left(\left(\left(-\dfrac{94}{7}\right)\sqrt{7}\right)-\dfrac{40}{3}-\dfrac{448}{5}-\dfrac{217}{9}\right)-\left(\left(\left(-15\right)\sqrt{7}\right)-\dfrac{43}{5}\right)-\left(\dfrac{448}{5}+55-\left(\left(-\dfrac{10}{3}\right)\sqrt{7}\right)-\left(\left(\dfrac{11}{2}\right)\sqrt{7}\right)-\left(\left(33\right)\sqrt{7}\right)\right)\right)\\ &=&\left(8-\left(\left(-\dfrac{315}{4}\right)\sqrt{7}\right)-\left(\left(0\right)\sqrt{7}\right)-\left(\left(\dfrac{195}{4}\right)\sqrt{7}\right)-\left(\left(53\right)\sqrt{7}\right)\right)-\left(-\dfrac{57}{7}-\left(\left(-4\right)\sqrt{7}\right)+56\right)+\dfrac{133}{2}-\left(\left(-\dfrac{52}{3}\right)\sqrt{7}+\left(\dfrac{111}{5}\right)\sqrt{7}+\left(\dfrac{195}{4}\right)\sqrt{7}+\left(\dfrac{265}{4}\right)\sqrt{7}\right)-\left(\left(27\right)\sqrt{7}+\left(-\dfrac{52}{3}\right)\sqrt{7}+\left(14\right)\sqrt{7}+\dfrac{50}{9}\right)+\dfrac{245}{4}-\left(\left(\dfrac{201}{4}\right)\sqrt{7}\right)-\left(\left(\left(-\dfrac{94}{7}\right)\sqrt{7}\right)-\dfrac{40}{3}-\dfrac{448}{5}-\dfrac{217}{9}\right)-\left(\left(\left(-15\right)\sqrt{7}\right)-\dfrac{43}{5}\right)-\left(\dfrac{448}{5}+55-\left(\left(-\dfrac{10}{3}\right)\sqrt{7}\right)-\left(\left(\dfrac{11}{2}\right)\sqrt{7}\right)-\left(\left(33\right)\sqrt{7}\right)\right)\\ &=&\dfrac{92461}{1260}+\left(-\dfrac{66019}{420}\right)\sqrt{7}\\ \end{eqnarray*} \begin{eqnarray*} X-Y &=&\left(\left(8-\left(\left(-\dfrac{63}{4}\right)\sqrt{175}\right)-\left(\left(0\right)\sqrt{175}\right)-\left(\left(\dfrac{39}{4}\right)\sqrt{175}\right)-\left(\left(\dfrac{53}{2}\right)\sqrt{28}\right)\right)-\left(-\dfrac{57}{7}-\left(\left(-2\right)\sqrt{28}\right)-\left(\left(-8\right)\sqrt{49}\right)\right)-\left(\left(-\dfrac{19}{2}\right)\sqrt{49}\right)-\left(\left(-\dfrac{26}{3}\right)\sqrt{28}+\left(\dfrac{37}{5}\right)\sqrt{63}+\left(\dfrac{39}{4}\right)\sqrt{175}+\left(\dfrac{53}{4}\right)\sqrt{175}\right)-\left(\left(9\right)\sqrt{63}+\left(-\dfrac{26}{3}\right)\sqrt{28}+\left(7\right)\sqrt{28}+\dfrac{50}{9}\right)\right)-\left(\left(\left(\dfrac{35}{4}\right)\sqrt{49}\right)-\left(\left(\dfrac{67}{4}\right)\sqrt{63}\right)-\left(\left(\left(-\dfrac{47}{7}\right)\sqrt{28}\right)-\dfrac{40}{3}-\left(\left(\dfrac{64}{5}\right)\sqrt{49}\right)-\left(\left(\dfrac{31}{9}\right)\sqrt{49}\right)\right)-\left(\left(\left(-3\right)\sqrt{175}\right)-\dfrac{43}{5}\right)-\left(\left(\left(\dfrac{64}{5}\right)\sqrt{49}\right)-\left(\left(-\dfrac{55}{7}\right)\sqrt{49}\right)-\left(\left(-\dfrac{2}{3}\right)\sqrt{175}\right)-\left(\left(\dfrac{11}{6}\right)\sqrt{63}\right)-\left(\left(\dfrac{33}{5}\right)\sqrt{175}\right)\right)\right)\\ &=&\left(\left(8-\left(\left(-\dfrac{315}{4}\right)\sqrt{7}\right)-\left(\left(0\right)\sqrt{7}\right)-\left(\left(\dfrac{195}{4}\right)\sqrt{7}\right)-\left(\left(53\right)\sqrt{7}\right)\right)-\left(-\dfrac{57}{7}-\left(\left(-4\right)\sqrt{7}\right)+56\right)+\dfrac{133}{2}-\left(\left(-\dfrac{52}{3}\right)\sqrt{7}+\left(\dfrac{111}{5}\right)\sqrt{7}+\left(\dfrac{195}{4}\right)\sqrt{7}+\left(\dfrac{265}{4}\right)\sqrt{7}\right)-\left(\left(27\right)\sqrt{7}+\left(-\dfrac{52}{3}\right)\sqrt{7}+\left(14\right)\sqrt{7}+\dfrac{50}{9}\right)\right)-\left(\dfrac{245}{4}-\left(\left(\dfrac{201}{4}\right)\sqrt{7}\right)-\left(\left(\left(-\dfrac{94}{7}\right)\sqrt{7}\right)-\dfrac{40}{3}-\dfrac{448}{5}-\dfrac{217}{9}\right)-\left(\left(\left(-15\right)\sqrt{7}\right)-\dfrac{43}{5}\right)-\left(\dfrac{448}{5}+55-\left(\left(-\dfrac{10}{3}\right)\sqrt{7}\right)-\left(\left(\dfrac{11}{2}\right)\sqrt{7}\right)-\left(\left(33\right)\sqrt{7}\right)\right)\right)\\ &=&\left(\dfrac{2657}{126}+\left(-\dfrac{2558}{15}\right)\sqrt{7}\right)-\left(\dfrac{9413}{180}+\left(\dfrac{1121}{84}\right)\sqrt{7}\right)\\ &=&\dfrac{2657}{126}+\left(-\dfrac{2558}{15}\right)\sqrt{7}+-\dfrac{9413}{180}+\left(-\dfrac{1121}{84}\right)\sqrt{7}\\ &=&-\dfrac{4369}{140}+\left(-\dfrac{25743}{140}\right)\sqrt{7}\\ \end{eqnarray*} \begin{eqnarray*} X\times Y &=&\left(\left(8-\left(\left(-\dfrac{63}{4}\right)\sqrt{175}\right)-\left(\left(0\right)\sqrt{175}\right)-\left(\left(\dfrac{39}{4}\right)\sqrt{175}\right)-\left(\left(\dfrac{53}{2}\right)\sqrt{28}\right)\right)-\left(-\dfrac{57}{7}-\left(\left(-2\right)\sqrt{28}\right)-\left(\left(-8\right)\sqrt{49}\right)\right)-\left(\left(-\dfrac{19}{2}\right)\sqrt{49}\right)-\left(\left(-\dfrac{26}{3}\right)\sqrt{28}+\left(\dfrac{37}{5}\right)\sqrt{63}+\left(\dfrac{39}{4}\right)\sqrt{175}+\left(\dfrac{53}{4}\right)\sqrt{175}\right)-\left(\left(9\right)\sqrt{63}+\left(-\dfrac{26}{3}\right)\sqrt{28}+\left(7\right)\sqrt{28}+\dfrac{50}{9}\right)\right)\times\left(\left(\left(\dfrac{35}{4}\right)\sqrt{49}\right)-\left(\left(\dfrac{67}{4}\right)\sqrt{63}\right)-\left(\left(\left(-\dfrac{47}{7}\right)\sqrt{28}\right)-\dfrac{40}{3}-\left(\left(\dfrac{64}{5}\right)\sqrt{49}\right)-\left(\left(\dfrac{31}{9}\right)\sqrt{49}\right)\right)-\left(\left(\left(-3\right)\sqrt{175}\right)-\dfrac{43}{5}\right)-\left(\left(\left(\dfrac{64}{5}\right)\sqrt{49}\right)-\left(\left(-\dfrac{55}{7}\right)\sqrt{49}\right)-\left(\left(-\dfrac{2}{3}\right)\sqrt{175}\right)-\left(\left(\dfrac{11}{6}\right)\sqrt{63}\right)-\left(\left(\dfrac{33}{5}\right)\sqrt{175}\right)\right)\right)\\ &=&\left(\left(8-\left(\left(-\dfrac{315}{4}\right)\sqrt{7}\right)-\left(\left(0\right)\sqrt{7}\right)-\left(\left(\dfrac{195}{4}\right)\sqrt{7}\right)-\left(\left(53\right)\sqrt{7}\right)\right)-\left(-\dfrac{57}{7}-\left(\left(-4\right)\sqrt{7}\right)+56\right)+\dfrac{133}{2}-\left(\left(-\dfrac{52}{3}\right)\sqrt{7}+\left(\dfrac{111}{5}\right)\sqrt{7}+\left(\dfrac{195}{4}\right)\sqrt{7}+\left(\dfrac{265}{4}\right)\sqrt{7}\right)-\left(\left(27\right)\sqrt{7}+\left(-\dfrac{52}{3}\right)\sqrt{7}+\left(14\right)\sqrt{7}+\dfrac{50}{9}\right)\right)\times\left(\dfrac{245}{4}-\left(\left(\dfrac{201}{4}\right)\sqrt{7}\right)-\left(\left(\left(-\dfrac{94}{7}\right)\sqrt{7}\right)-\dfrac{40}{3}-\dfrac{448}{5}-\dfrac{217}{9}\right)-\left(\left(\left(-15\right)\sqrt{7}\right)-\dfrac{43}{5}\right)-\left(\dfrac{448}{5}+55-\left(\left(-\dfrac{10}{3}\right)\sqrt{7}\right)-\left(\left(\dfrac{11}{2}\right)\sqrt{7}\right)-\left(\left(33\right)\sqrt{7}\right)\right)\right)\\ &=&\left(\dfrac{2657}{126}+\left(-\dfrac{2558}{15}\right)\sqrt{7}\right)\left(\dfrac{9413}{180}+\left(\dfrac{1121}{84}\right)\sqrt{7}\right)\\ &=&\dfrac{25010341}{22680}+\left(-\dfrac{123402207618}{14288400}\right)\sqrt{7}+\left(-\dfrac{1433759}{630}\right)\sqrt{49}\\ &=&-\dfrac{30266723430}{2041200}+\left(-\dfrac{123402207618}{14288400}\right)\sqrt{7}\\ \end{eqnarray*}