If $$x=2+\sqrt2$$​, then what will be the value of $$x^2-4x+4$$​ ?

Correct option is C

Given:

​$$x = 2 + \sqrt{2}$$​​

We need to find the value of $$x^2 - 4x + 4.$$​​

Formula Used:

(a + b)² = a² + b² + 2ab

Solution:

​$$x^2 - 4x + 4 = 4 + 4\sqrt{2} +2 - 8 - 4\sqrt{2} +4$$​​​​

​$$= 6 + 4\sqrt{2} - 8 - 4\sqrt{2} + 4$$​

​$$= (6 - 8 + 4) + (4\sqrt{2} - 4\sqrt{2}) =2 + 0 = 2$$ 

Alternate Method: 

$$x = 2 + \sqrt 2 \\ \ \\ x -2 = \sqrt 2$$ 

Squaring both side;

​$$(x - 2)^2 = (\sqrt2)^2 \\ \ \\ x^2 -4x +4 = 2$$​​