Incorrect values of the variable, such as those that are introduced as a result of the squaring process are called extraneous solutions. Extraneous solutions may look like the real solution, but you can identify them because they will not create a true statement when substituted back into the original equation.
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.
Beside this, Why do extraneous solutions sometimes occur in equations with rational expressions?
b. Why do extraneous solutions sometimes occur in the process of solving rational or radical equations? … Answer: Squaring both sides of a square-root radical equation introduces two solutions (the positive and negative) that might be the solution to the equation.
Likewise, Do rational equations have extraneous solutions?
Whenever you solve a rational equation, always check your (interim) solution against the denominators (and their disallowed values) from the original equation. It is entirely possible that a problem will have an invalid (that is, an “extraneous”) solution. This is especially true on tests. So always check!
Also, What does it mean to check for extraneous solutions?
Extraneous solutions are values that we get when solving equations that aren’t really solutions to the equation.
What is the significance of an extraneous root?
a root, or solution, of an intermediate equation—an equation obtained in the process of solving a given equation—that is not a root of the given equation. Extraneous roots appear because in solving an equation we cannot always pass to equivalent equations when we simplify it.
17 Related Question Answers Found
How do you check for extraneous solutions in a rational equation?
If a solution is a restriction, then it is not part of the domain and is extraneous. When multiplying both sides of an equation by an expression, distribute carefully and multiply each term by that expression. If all of the resulting solutions are extraneous, then the original equation has no solutions.
Do quadratic equations have extraneous solutions?
Extraneous solutions: multiplication This quadratic equation has two solutions, − 2 and 0. But if zero is substituted for x into the original equation, the result is the invalid equation 2 = 0.
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.
How do you find the extraneous solution of a rational equation?
If a solution is a restriction, then it is not part of the domain and is extraneous. When multiplying both sides of an equation by an expression, distribute carefully and multiply each term by that expression. If all of the resulting solutions are extraneous, then the original equation has no solutions.
How do you know if a solution is extraneous or 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 causes extraneous solutions when solving radical equations?
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 does it mean to have an extraneous solution for a rational equation?
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.
How do you know if an answer is extraneous?
Direct link to A/V’s post “Plug in your solution back into the original equat…” 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.
How do you check for extraneous solutions?
To find whether your solutions are extraneous or not, you need to plug each of them back in to your given equation and see if they work. It’s a very annoying process sometimes, but if employed properly can save you much grief on tests or quizzes.
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 logarithmic equations sometimes have extraneous solutions?
Extraneous solutions are caused by actions that can take a false (or undefined) equation to a true equation. Extraneous solutions are discarded, since they are not solutions of the original equation.
What does it mean to have an extraneous solution?
Extraneous solutions are values that we get when solving equations that aren’t really solutions to the equation.
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