What is an extraneous solution?

An extraneous solution is a solution to an equation that does not actually satisfy the original equation. This can occur when solving equations with multiple steps, such as when taking the square root of both sides or when simplifying expressions.

Extraneous solutions often arise in equations involving radicals, logarithms, or rational expressions. When solving these types of equations, it is important to check the solutions in the original equation to ensure they are valid.

One common mistake that leads to extraneous solutions is squaring both sides of an equation. This can introduce additional solutions that do not satisfy the original equation, resulting in an extraneous solution.

To avoid extraneous solutions, it is important to carefully follow the rules of algebra when solving equations and always check the solutions in the original equation to verify their validity.