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.

Examples of Extraneous Solution

• Consider the equation .

Square both sides and solve the equation for y, we get, y = 1, 25.

Check that only y = 25 statisfies 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

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