Question

$<var>se x =1+\sqrt{2},entao x^{2} -2x+1 e igual a:</var>$[tex]

Answer 1

Temos que:

 

$\text{x}=1+\sqrt{2}$

 

Desta maneira: 

 

$\text{x}^2=(1+\sqrt{2})^2=3+2\sqrt{2}$

 

$2\text{x}=2\cdot(1+\sqrt{2})=2+2\sqrt{2}$

 

Logo:

 

$\text{x}^2-2\text{x}+1=3+2\sqrt{2}-2-2\sqrt{2}+1=2$

Answer 2

Fatorando x² - 2x + 1:

 

 $x^2 - 2x + 1 = \\ (x - 1)^2 =$

 

 Substituindo o valor de x...

 

$x^2 - 2x + 1 = \\ (x - 1)^2 = \\ (1 + \sqrt{2} - 1)^2 = \\ (\sqrt{2})^2 = \\ \boxed{2}$