solve by completing square:

^{x2 - (root2 + 1)x + root 2=0}

x² - ( root2 + 1)x + root2= 0

= x² - 2. (1/2) . (root2 + 1). x + {(root2 + 1)/2}² - (root2 + 1)²/4 + root2= 0

= {x - (root2 + 1)/2}² = (root2+ 1)²/4 - root2 = ( 2 + 1 + 2root2)/4 - root2 = 3 -2root2/4= (root2 - 1)²/4

= x - (root2 + 1)/2= +(root2-1)/2 , or , -(root2 - 1)/2

= x = root2 , or, 1

ANS= x = root2 or 1.