Expert: Scott A Wilson - 9/19/2010

Question
What is the difference between a wrong answer and an extraneous solution?
What algebraic procedure can create an extraneous solution? (My teacher told me that when you do them, you need to remember to check for extraneous solutions.)

Answer
An extraneous answer is one that pops up but isn't really the answer.

For example, if a triangle were looked at with on side 3 and the other 4, the length of the hypotenuse would be 5.  The equation is
c = √(a²+b²), so c = √(3²+4²) = √(9+16) = √25.
This is the same as c = ±5.  The extraneous answer is c = -5.

Lengths are known to be positive, so -5 is an extraneous answer.