Explanation

√(x - 1)^2 + √(3 - x)^2

Since 1 < x < 2, we can simplify the expressions inside the square roots:

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

(3 - x)^2 = (3 - x)(3 - x) = 9 - 6x + x^2

Now, add the two expressions:

x^2 - 2x + 1 + 9 - 6x + x^2

= 2x^2 - 8x + 10

Take the square root of the result:

√(2x^2 - 8x + 10)

Since 1 < x < 2, we can plug in x = 1 and x = 2 to find the maximum and minimum values:

At x = 1: √(2 - 8 + 10) = √4 = 2

At x = 2: √(8 - 16 + 10) = √2

So, the minimum value of the expression is 2, which occurs when x = 1.

Therefore, the correct answer is: 2