Vacuous truth

Analysis. For any real $x$, $x^2\ge0$, so the hypothesis $x^2<0$ is never satisfied. The implication $(x^2<0\Rightarrow x>0)$ is vacuously true for every $x$.

Conclusion. The universal statement is true (vacuously).

Remark. Vacuous truth is a subtle but important feature of universal statements over empty domains.