What is an extraneous solution and why do they occur in logarithmic equations?
An extraneous solution is a number for which an original equation is either undefined or false, but for which a later equation is true. Extraneous solutions are caused by actions that can take a false (or undefined) equation to a true equation.
How do you get 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.
What does it mean for a solution to be extraneous?
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?
Definition of extraneous 1 : existing on or coming from the outside extraneous light. 2a : not forming an essential or vital part extraneous ornamentation. b : having no relevance an extraneous digression. 3 : being a number obtained in solving an equation that is not a solution of the equation extraneous roots.
Why do extraneous solutions sometimes occur and don’t work in the original form of the 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.
What does the solution is extraneous mean?
Do absolute value functions have extraneous solutions?
It means that thing inside the absolute value A equals either positive B or negative B. So equals either the expression on the other side or the expression on the other side with a negative sign in front of it. Sometimes this will give us extraneous solutions. So this is an odd thing about absolute value equations.
What is the meaning when having an extraneous solution?
Extraneous solutions are values that we get when solving equations that aren’t really solutions to the equation.
Why do extraneous roots occur?
In general, extraneous solutions arise when we perform non-invertible operations on both sides of an equation. Squaring (or raising to any other even power) is a non-invertible operation. Solving equations involving square roots involves squaring both sides of an equation.
What type of problems have extraneous solutions?
Rational equations- If any potential solution makes any denominator’s value equal zero than the potential solution is an extraneous one. Equations where you raise both sides to an even power, that is, equations with even roots in them.
What is an extraneous solution in absolute value?
An extraneous solution is a solution that, when plugged back in to the original equation, does not work. Extraneous solutions can occur when dealing with absolute values or quadratics.
Why do extraneous solutions occur in math?
“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. That’s a fine thing to do as long as we’re aware of the meaning of what we’re doing,…
Is -8 an extraneous solution to the problem?
Therefore, -8 is an extraneous solution. In other cases, the problem itself might set restrictions on the solution. Find all two digit numbers such that when the number is squared, and ten times the number is subtracted, the result is 11. This problem leads to the quadratic: x 2 – 10x – 11 = 0 x = 11 or x = -1.
What is an example of an extraneous square root?
For example, the square roots of 4 are 2 and -2. However, when we write radical notation, we are, be definition, referring to the principle square root, which is the positive value. Thus, a solution may be extraneous because it results from using a negative square root instead of the principle square root.
How do you find the solutions to quadratic equations?
Those “solutions” appear because in the process of solving the equation you do things which are not reversible. For example, suppose you want to solve the (easy!) equation $$x=-1.$$ If you square both sides, you obtain $$x^2=1,$$ and this can be solved using the formula for roots of a quadratic equation (!) to find the two solutions $1$ and $-1$.