Check:rebo1984 said:Hi everyone,
What is the solution set of the equation: sqrt{x+2}= x-4
I got 2 and 7.
Is it correct or is it just 7. If so why?
Thanks:)
An extraneous solution is a solution to an equation that does not satisfy the original equation. This can happen when solving equations involving square roots because taking the square root of a number can introduce an additional solution that does not actually work in the original equation.
To identify an extraneous solution, you can plug the solution back into the original equation and see if it satisfies the equation. If the solution does not work, then it is extraneous. Another way to identify an extraneous solution is to check if the solution makes the radicand (the number inside the square root symbol) negative, which is not allowed.
Extraneous solutions occur in equations involving square roots because taking the square root of a number can introduce an additional solution that does not actually work in the original equation. This can happen because when we square both sides of an equation to solve for the variable, we are essentially introducing a new equation that may have additional solutions.
To avoid getting extraneous solutions, you can check your solutions by plugging them back into the original equation. Additionally, you can also simplify the equation before taking the square root, which can help eliminate some potential extraneous solutions.
Yes, extraneous solutions are always incorrect because they do not satisfy the original equation. However, they can still provide useful information in the problem-solving process, such as indicating that there may be an error in the solution or that the equation may have no real solutions.