What is extraneous solution?

An extraneous solution is a solution to an equation that is mathematically correct but does not satisfy the original problem. This can occur when solving equations with multiple steps and manipulating both sides of the equation.

Extraneous solutions often arise when there are restrictions or limitations on the variables in the original problem. For example, taking the square root of both sides of an equation can introduce extraneous solutions if the original equation only allowed for positive values of the variable.

It is important to always check for extraneous solutions when solving equations, especially when working with equations involving radicals, logarithms, or absolute values. This can help ensure that the solutions found are valid and applicable to the original problem.