Answer:
an apparent solution that does not satisfy the original equation
Step-by-step explanation:
Usually, an extraneous solution is introduced by the solution process. Sometimes it takes the form of multiplying an equation by 0, often the result of eliminating the denominators of rational functions.
Other times, it takes the form of adding branches to a function that are unintended or undefined. (Squaring a square root will often introduce "solutions" that require the square root to be a negative value.) The attached graph shows that x=4 is an extraneous solution to ...
√x = x-6
It shows up when the equation is squared:
x = x² -12x +36 ⇒ (x -9)(x -4) = 0
The "solution" x=4 is extraneous because it does not satisfy the original equation.
As in this graphed example, using graphical methods to find solutions can often avoid extraneous solutions.
