Originally Posted by

**mr fantastic** There is an implied restriction on x in this working that will cause one of the branches of this hyperbola to be rejected (that branch is an extraneous solution and is introduced by the squaring process). But I don't have the time to read through it. However, it is sufficient to test a simple point on each branch and reject the branch that contains the point that fails to satisfy the original equation.

Personally, I favour the approach of moving a radical to one side first before squaring. The implied restriction is a lot more obvious. If I have time later, I might show the first few steps.