Resposta :
Temos que:
[tex]\text{x}=1+\sqrt{2}[/tex]
Desta maneira:
[tex]\text{x}^2=(1+\sqrt{2})^2=3+2\sqrt{2}[/tex]
[tex]2\text{x}=2\cdot(1+\sqrt{2})=2+2\sqrt{2}[/tex]
Logo:
[tex]\text{x}^2-2\text{x}+1=3+2\sqrt{2}-2-2\sqrt{2}+1=2[/tex]
Fatorando x² - 2x + 1:
[tex]x^2 - 2x + 1 = \\ (x - 1)^2 =[/tex]
Substituindo o valor de x...
[tex]x^2 - 2x + 1 = \\ (x - 1)^2 = \\ (1 + \sqrt{2} - 1)^2 = \\ (\sqrt{2})^2 = \\ \boxed{2}[/tex]