extraneous solution


Definition of Extraneous Solution

  • Extraneous Solution is a solution of the simplified form of an equation that does not satisfy the original equation.
Example of Extraneous Solution

  • Consider the equation .
    Squaring both sides and solving the equation for y, we get, y = 1, 25.
    Check that only y = 25 satisfies the original equation, not y = 1. So, y = 1 is an extraneous solution.  
                                               

Solved Example on Extraneous Solution

Solve  and check whether the solution is extraneous.
Choices:
A. Yes
B. No
Correct Answer: B
Solution:
Step 1:
Step 2:                          
Step 3:  
Step 4: x = 144
Step 5: Substitute the value of x in the original equation.
, so, x = 144 is an extraneous solution.

Related Terms for Extraneous Solution

  • Solution
  • Equation