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How do you know if a solution is extraneous?
To tell if a “solution” is extraneous you need to go back to the original problem and check to see if it is actually a solution. 1/(x-1) = x/(x2-1) Solving this algebraically gives x = 1. But this can't be a solution as both denominators are zero when x is 1. This equation has no solution.
What does it mean when a solution is extraneous?
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.
What causes an extraneous solution?
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.
What is an extraneous root?
Extraneous Root. More ... A solution to an equation that SEEMS to be right, but when we check it (by substituting it into the original equation) turns out NOT to be right. Example: you work on an equation and come up with two roots (where it equals zero): “a” and “b”.
What is an extraneous solution to a radical equation?
In general, extraneous solutions arise when we perform non-invertible operations on both sides of an equation. (That is, they sometimes arise, but not always.) Squaring (or raising to any other even power) is a non-invertible operation. ... The equations: x1=4 and x=5, have exactly the same set of solutions.
What is an extraneous solution example?
Extraneous Solutions. 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 is an extraneous solution definition?
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.
How do you know if it is an extraneous solution?
To tell if a “solution” is extraneous you need to go back to the original problem and check to see if it is actually a solution. 1/(x-1) = x/(x2-1) Solving this algebraically gives x = 1. But this can't be a solution as both denominators are zero when x is 1. This equation has no solution.
Why do extraneous solutions occur?
”Extraneous” solutions occur because when we analyze problems, simplify equations and perform various other processes to solve stuff we often do manipulations that change the problem by a little, or by a lot. ... When you have an equation, and you multiply both sides by 23, the result is equivalent to the original.
Do Radical Equations have extraneous solutions?
When you square a radical equation you sometimes get a solution to the squared equation that is not a solution to the original equation. Such an equation is called an extraneous solution. Remember to always check your solutions in the original equation to discard the extraneous solutions.
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