Zero Equals One

Resolution
This is a falsidical paradox arising from incorrect reasoning about the nature of square roots.

Explanation
While this line is correct:
 * $\left({4 - \dfrac 9 2}\right)^2 - \left({5 - \dfrac 9 2}\right)^2$

note that:
 * $4 - \dfrac 9 2 = -\dfrac 1 2$

but:
 * $5 - \dfrac 9 2 = \dfrac 1 2$

and the paradox is resolved.