If (a + b)^1/2 = (a - b )^-1/2 why must a^2 - b^2 = 1 must be true?

If Set X has x members and yet Y has y members, Set Z consists of all members that are in either set X or set Y with the exception of the k common members (k > 0), then why must x + y - 2k must equal the number of members in set Z?