Bonsoir,
[tex]x=\sqrt{2} -1\\\\x^2=(\sqrt{2} -1)^2=2-2\sqrt{2} +1=3-2\sqrt{2} \\\\Si\ x\leq x^2\\\Longrightarrow\ \sqrt{2} -1\leq 3-2\sqrt{2}\\\Longrightarrow\ 3\sqrt{2} \leq 4\\\\\Longrightarrow\ (3\sqrt{2})^2\leq 4^2\\\Longrightarrow\ 9*2\leq 16\\\Longrightarrow\ 18\leq 16\ est\ faux\\\\\boxed{\Longrightarrow\ x^2< x}\\\\\boxed{\Longrightarrow\ x< \sqrt{x} }\\\\\\\boxed{\Longrightarrow\ x^2< x< \sqrt{x} }\\\\\\[/tex]
