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.
Squaring on both sides, we have:
in other wrds, solution of an simplified equation that does not solve the original equation, eg.
ReplyDeletesqrt(x) = -1 * => squaring leads to, x = 1 which is real! the solution here was algebraically derived, but it does not conform to the original hypothesis *.
true...the point i wanted to make was to be aware of extraneous solutions during manipulation. Of course, a simple way to weed of the extraneous solutions would be to test them by pluggin them into the original equation.
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