Bonjour Chachou942
Exercice 1
[tex]a)\ 1\ \textless \ x\ \textless \ 7\Longleftrightarrow x\in\ ]1;7[\\\\b)\ x\le5\Longleftrightarrow x\in\ ]-\infty;5][/tex]
Exercice 2
[tex]a)\ 7,82\times10^5=782\ 000\\\\7,82\times10^5\in\boxed{\mathbb{N}}\\\\b)\ (\sqrt{\dfrac{3}{7}}+\sqrt{\dfrac{7}{3}})^2=(\sqrt{\dfrac{3}{7}})^2+2\sqrt{\dfrac{3}{7}}\times\sqrt{\dfrac{7}{3}}+(\sqrt{\dfrac{7}{3}})^2\\\\\\(\sqrt{\dfrac{3}{7}}+\sqrt{\dfrac{7}{3}})^2=\dfrac{3}{7}+2\sqrt{\dfrac{3}{7}\times\dfrac{7}{3}}+\dfrac{7}{3}}\\\\\\(\sqrt{\dfrac{3}{7}}+\sqrt{\dfrac{7}{3}})^2=\dfrac{3}{7}+2\times1+\dfrac{7}{3}}\\\\\\(\sqrt{\dfrac{3}{7}}+\sqrt{\dfrac{7}{3}})^2=\dfrac{3}{7}+2+\dfrac{7}{3}}[/tex]
[tex]\\\\\\(\sqrt{\dfrac{3}{7}}+\sqrt{\dfrac{7}{3}})^2=\dfrac{9}{21}+\dfrac{49}{21}}+2\\\\\\(\sqrt{\dfrac{3}{7}}+\sqrt{\dfrac{7}{3}})^2=\dfrac{58}{21}+2\\\\\\(\sqrt{\dfrac{3}{7}}+\sqrt{\dfrac{7}{3}})^2=\dfrac{58}{21}+\dfrac{42}{21}\\\\\\(\sqrt{\dfrac{3}{7}}+\sqrt{\dfrac{7}{3}})^2=\dfrac{100}{21}\\\\\\(\sqrt{\dfrac{3}{7}}+\sqrt{\dfrac{7}{3}})^2\in\boxed{\mathbb{Q}}[/tex]
