The question as written, 2sqrt((x−1)3) − 4 = 0, leads to x = 1 + [3]4, which is approximately 2.587. This value is not among the given options.

$$2\sqrt{(x-1)^2} - 4 = 0$$

Add 4 to both sides:

$$2\sqrt{(x-1)^2} = 4$$

$$\sqrt{(x-1)^2} = \frac{4}{2}$$ $$\sqrt{(x-1)^2} = 2$$

Recall that $\sqrt{a^2} = |a|$.

$$|x-1| = 2$$

This means that $x-1$ can be 2 or $x-1$ can be $-2$.

Case 1:

$$x-1 = 2$$

Add 1 to both sides:

$$x = 2 + 1$$ $$x = 3$$

Case 2:

$$x-1 = -2$$

Add 1 to both sides:

$$x = -2 + 1$$ $$x = -1$$

The possible values for $x$ are 3 and $-1$.
The given options are A) 3 and B) 2.
Since $x=3$ is one of the solutions and is listed as option A, this is the most probable intended answer.

The final answer is $\text{A) 3}$.