FAQ: What is an extraneous solution?

How do you know if a solution is extraneous?

Plug in your solution back into the original equation. If it shows a false meaning (e.g 2=3) or if the value is undefined (n/0), then it’s extraneous.

What is an extraneous solution example?

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. Example 1: Solve for x, 1x − 2+1x + 2=4(x − 2)(x + 2).

What can cause an extraneous solution?

The reason extraneous solutions exist is because some operations produce ‘extra’ answers, and sometimes, these operations are a part of the path to solving the problem. When we get these ‘extra’ answers, they usually don’t work when we try to plug them back into the original problem.

What is an extraneous solution to a radical equation?

In math, an extraneous solution is a solution that emerges during the process of solving a problem but is not actually a valid solution. You can only find out whether or not a solution is extraneous by plugging the solution back into the original equation.

Can an extraneous solution be negative?

Extraneous solutions are not necessarily outside the domain. But they can appear as extra solutions when we square both sides of an equation, because when we square an equation, we would get the same result whether the original equation was positive or negative.

What does extraneous mean?

1: existing on or coming from the outside extraneous light. 2a: not forming an essential or vital part extraneous ornamentation.

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Which is the best description of an extraneous solution?

In mathematics, an extraneous solution (or spurious 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.

Why do you need to check for extraneous solutions?

You only need to worry about the extraneous root in the case of a quadratic equation if you made the equation quadratic by multiplying by a variable. Any time you square a negative number or a variable (which may be negative), you risk losing information by making it positive.

Why do absolute value equations have extraneous solutions?

Right from the start, you can say that any negative value of x will be an extraneous solution because the absolute value of a number can only be positive. This solution will be extraneous because it implies that the absolute values of 4 is negative, which is false.

Can you have two extraneous solutions?

In the first step both sides of the equation are squared. We call x=-2 an extraneous solution. While the equation x2-6=x does indeed have these two solutions, x=-2 is not a solution of the original equation because ln(-2) does not exist (as a real number, at least). Thus x=-2 is an extraneous solution.

How do you get rid of radicals?

To solve it you simply apply our general principle: To solve an equation figure out what bothers you and then do the same thing on both sides of the equation to get rid of it. To get rid of a radical you take it to a power that will change the rational exponent to a natural number.

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Why is it important to check all solutions to radical equations?

When a power is taken on both sides of an equation, the resulting solutions might not check in the original radical equation. You must check solutions by substituting in the values into the original equation and verifying that it produces a true statement.

How do you check for extraneous roots?

Example: you work on an equation and come up with two roots (where it equals zero): “a” and “b”. When you put “a” into the original equation it becomes zero, but when you put in “b” it doesn’t. So “b” is an extraneous root. This often happens when we square both sides during our solution.

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