What is a extraneous solution?

An extraneous solution is a solution to an equation that is not valid in the original problem. This can occur when solving equations that involve rational expressions, square roots, or logarithms.

Extraneous solutions can arise when there are restrictions on the domain of the equation, and a solution that is found is outside of this domain. It can also occur when squaring both sides of an equation, which can introduce additional solutions that are not valid.

It is important to check for extraneous solutions when solving equations, especially when working with expressions that involve variables. One way to do this is to substitute the solution back into the original equation and see if it is true.

Extraneous solutions can be a common pitfall in algebraic problem-solving, so it is important to be aware of this possibility and to always double-check your solutions.