The commutative property ... of square roots

The problem is asking is there is any solution of x such that both x^1/2=y^1/2 and x≠y are satisfied.

We take the first equation: x^1/2=y^1/2

And we take the 2nd power of each: x=y

Uh-oh, that breaks the second rule, which says the following: x≠y

So there are 0 solutions.

$\begin{aligned} \sqrt{x} &= \sqrt{y} \\ (\sqrt{x})^2 &= (\sqrt{y})^2 \\ x &= y \end{aligned}$

$\text{Since, } x=y \text{ is the only solution, but that condition is not true. Thus there are no solutions} \implies \boxed{0}$