Extraneous Solution Meaning Math

It is not actually a solution and is not inherent in the problem itself but is introduced by what you do.

Extraneous solution meaning math. We want x to be a genuine function which means it can t output two numbers on one input. Extraneous solutions are solutions which are obtained algebraically but even though they are found algebraically they don t work in the context of the problem. In case you are not familiar with the concept an extraneous solution also called an extraneous root is a solution you get in the process of solving that turns out not to be a solution of the original equation. Here are some of the reasons a problem might have extraneous solutions.

Solve for x 1 x 2 1 x 2 4 x 2 x 2. Extraneous means not relevant to the problem so we don t accept them as solutions. So the equation has no solution at all. Extraneous solution is a solution of the simplified form of an equation that does not satisfy the original equation.

However when we try to check the solution x 2 it causes the first and last denominators to become 0. X 1 is called an extraneous solution which is really not a solution at all. In mathematics an extraneous solution is a solution such as that to an equation that emerges from the process of solving the problem but is not a valid solution to the problem. But 2 is excluded from the domain of the original equation because it would make the denominator of one of the fractions zero and division by zero is not allowed.

So if you plug 1 into your equation it becomes. Both are frequently the consequence of performing operations that are not invertible for some or all values of the variables which prevents the chain of logical implications in the proof. A missing solution is a solution that is a valid solution to the problem but disappeared during the process of solving the problem. An extraneous solution is a root of a transformed equation that is not a root of the original equation because it was excluded from the domain of the original equation.

Generally the x notation refers to the principal root of x when it s used in algebraic equations. When you multiply through by the lcd and solve the resulting quadratic equation you get solutions x 2 and x 1. For each reason i ll give an example.