Extraneous Solution is a solution of the simplified form of an equation that does not satisfy the original equation.
Video Examples: Extraneous solution when solving radical equations
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
Ques: 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.