Algebra Facts
Common Types of Mistakes: Extraneous Solutions |

Sometimes a method used to solve an equation gives
Solving this equation leads (initially) to two solutions. In the first step both sides of the equation are squared.
Note that both x=1 and x=-2 are solutions of the equation x
We call x=-2 an Sometimes extraneous solutions arise purely from domain considerations.
The first step in solving this equation is to undo the natural logarithms by applying the exponential function to both sides.
While the equation x The domain can also be a reason to reject extraneous solution in applied ("word") problems in which a solution must (for example) be positive. If you solve an equation arising in a problem asking (say) for the lengths of the sides of a pig pen that maximizes the area of the pen with a limited amount of fence material, you can reject any negative length possible answers right away. Mistakes arising from extraneous solutions for equations can be subtle. Know to look for them in situations like those mentioned on this page. |

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