Question

please explain your answer properly

Answer 1

Given, x = root 2 + 1     ------------------- (1)

           1/x = 1/root 2 + 1

                = root 2 - 1/(root 2-1)(root 2 + 1)

               = root 2 - 1/1

         1/x = root 2 - 1         -------------- (2)

From (1) and (2), we get

x - 1/x = (root 2 + 1) - (root 2 -1)

          = root 2 + 1 - root 2 + 1
 
          = 2


(x - 1/x)^2 = (2)^2

                 = 4.


Hope this helps!