Bonsoir,
Résoudre l'équation: [tex]x(x+1)=\sqrt{2}\left(\sqrt{2}+1\right)[/tex]
[tex]x(x+1)=\sqrt{2}\left(\sqrt{2}+1\right)\\\\x^2+x=2+\sqrt{2}\\x^2+x-2-\sqrt{2}=0\\\\x^2-\left(\sqrt{2}\right)^2+x-\sqrt{2}=0\\ \rightarrow a^2-b^2=(a-b)(a+b)\\ \left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)+x-\sqrt{2}=0\\ \left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)+\left(x-\sqrt{2}\right)=0\\ \left(x-\sqrt{2}\right)\left(x+\sqrt{2}+1\right)=0\\\\A\times B=0\text{ si }A=0\text{ ou }B=0\\x-\sqrt{2}=0\quad ou\quad x+\sqrt{2}+1=0\\x=\sqrt{2}\quad ou\quad x=-\left(\sqrt{2}+1\right)\\x=\sqrt{2}\quad ou\quad x=-\sqrt{2}-1\\\\ \boxed{S=\left\{-\sqrt{2}-1;\sqrt{2}\right\}}[/tex]
