The value of the discriminant of the equation, x² - ($\sqrt{2}$ + 1)x + $\sqrt{2}$ = 0 is:

1. 3 + $2\sqrt{2}$

2. 1 - $2\sqrt{2}$

3. 3 - $2\sqrt{2}$

4. 2 - $\sqrt{2}$

Comparing x² - ($\sqrt{2}$ + 1)x + $\sqrt{2}$ = 0 with ax² + bx + c = 0 we get,

a = 1, b = -($\sqrt{2}$ + 1) and c = $\sqrt{2}$.

We know that,

$\Rightarrow D = b^2 - 4ac \\[1em] = [-(\sqrt{2} + 1)]^2 - 4 \times 1 \times (\sqrt{2}) \\[1em] = (\sqrt2)^2 + 2 \times \sqrt2 \times 1 + 1^2 - 4(\sqrt{2}) \\[1em] = 2 + 2\sqrt2 + 1 - 4\sqrt{2} \\[1em] = 3 - 2\sqrt2.$

Hence, option 3 is the correct option.