EXTRANEOUS SOLUTION

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.

Video Examples: Extraneous solution when solving radical equations

Example of Extraneous Solution

Consider the equation example of Extraneous Solution .
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: example of Extraneous Solution
Step 2: example Extraneous Solution
Step 3: examples of Extraneous Solution
Step 4: x = 144
Step 5: Substitute the value of x in the original equation.
define Extraneous Solution so, x = 144 is an extraneous solution.

Quick Summary

Extraneous solutions can occur when solving radical equations or equations involving rational expressions.
Always check your solutions by substituting them back into the original equation.
If a solution does not satisfy the original equation, it is an extraneous solution and should be discarded.

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🍎 Teacher Insights

Emphasize the importance of checking solutions in the original equation to avoid accepting extraneous solutions. Provide plenty of examples where extraneous solutions arise and demonstrate the substitution process clearly.

🎓 Prerequisites

Solving equations
Radical equations
Substitution
Basic algebra skills

Check Your Knowledge

Q1: Solve for x: sqrt(x + 3) = x - 3

x = 1, 6 x = 6 x = 1 No solution

Q2: Which of the following operations is most likely to introduce extraneous solutions?

Adding a constant to both sides Multiplying both sides by a constant Squaring both sides Dividing both sides by a non-zero constant

Frequently Asked Questions

Q: Why do extraneous solutions occur?
A: Extraneous solutions occur because certain operations, such as squaring both sides of an equation, can introduce solutions that do not satisfy the original equation. This happens because the operation is not reversible for all values.

Q: How do I identify an extraneous solution?
A: To identify an extraneous solution, substitute each solution you obtain back into the original equation. If the solution does not make the original equation true, it is an extraneous solution.