Simplify 2 \s \sqrt{x { } ^(2) -4x + 4} x^2 - 4x + 4 if x<2​

Question

Simplify
2

`\s \sqrt{x { } ^(2) -4x + 4}`
x^2 - 4x + 4 if x<2​

Answer 1

2-x

Explanation:

Vx^2-4x+4=Vx^2-2*x*2+2^2=V(x-2)^2=|x-2|

if x<2 then x-2<0 and |x-2|=2-x

Answer 2

2 - x

Explanation:

x² - 4x + 4

4 = (-2)*(-2)

- 4 = -2 -2

x² - 4x + 4 = (x - 2)(x - 2) = (x - 2)²

√[(x - 2)²] = |x - 2|

or abs(x-2) because value under the root should be positive

if x< 2, then |x-2| = -(x-2) = 2 -x