A Gotcha with squaring on both sides..

One of the things we often do while solving equations is square on both sides of the equation. Until today, it never occured to me that one could introduce extraneous solutions by doing so. Here is a simple example. Consider the equation .

Squaring on both sides, we have: , which leads to solutions: . Here, is an extraneous solution as a result of squaring on both sides. Be mindful of this fact when you solve equations.