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You need to check for extraneous solutions when solving equations containing variables in denominators or within radical expressions. These solutions may arise from introducing new roots or excluded values during manipulations, which need to be verified to ensure they are valid in the original equation.
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What is an example sentence of the word extraneous?
The lab technicians said that the stray hair found on the toilet seat was from a previous guest who'd stayed in the hotel room, and was totally extraneous to the investigation.Exactly what I saw that night, I'm not sure, but it was extraneous to this plane of existence, and it still gives me nightmares.All seem to make values depend on extraneous factors.Many people may not want all this extraneous software cluttering up their hard drive.
What is an extraneous conductive part?
An extraneous conductive part is any conductive object or material that comes into contact with electrical circuits or components, creating a potential safety hazard. These parts can unintentionally carry current, cause short circuits, or interfere with the normal operation of electrical systems. Proper grounding and insulation techniques are essential to prevent extraneous conductive parts from causing problems.
Why to use 84 microsiemens conductivity standard solution?
Standard solutions are used to check instruments and methods of analysis.
How do you prevent contaminating a specimen with extraneous micoorganisms?
To prevent contamination of a specimen with extraneous microorganisms, maintain a sterile working environment, use proper aseptic techniques, and handle the specimen carefully to avoid contact with surfaces or airborne contaminants. Additionally, ensure that all equipment used is properly sterilized before use.
Solutions of chemistry chapter solutions xii?
Can you please provide more specific information about the chemistry chapter or topic you need solutions for in class XII? This will help me provide you with the relevant information you are looking for.
What is the extraneous solution to w equals sqrt 7w?
An "extraneous solution" is not a characteristic of an equation, but has to do with the methods used to solve it. Typically, if you square both sides of the equation, and solve the resulting equation, you might get additional solutions that are not part of the original equation. Just do this, and check each of the solutions, whether it satisfies the original equation. If one of them doesn't, it is an "extraneous" solution introduced by the squaring.
In general when solving a radical equation should you first isolate the radical and then both sides?
It often helps to isolate the radical, and then square both sides. Beware of extraneous solutions - the new equation may have solutions that are not part of the solutions of the original equation, so you definitely need to check any purported solutions with the original equation.
What does extraneous mean What must you do to determine whether a solution is an extraneous solution?
Extraneous means extra and unnecessary. Extraneous solutions are values that can arise from the process of solving the equation but do not in fact satisfy the initial equation. These solutions occur most often when not all parts of the process of solving are not completely reversible - for example, if both sides of the equation are squared at some point.
Why is it necessary to check for extraneous solutions in radical equations?
1) When solving radical equations, it is often convenient to square both sides of the equation. 2) When doing this, extraneous solutions may be introduced - the new equation may have solutions that are not solutions of the original equation. Here is a simple example (without radicals): The equation x = 5 has exactly one solution (if you replace x with 5, the equation is true, for other values, it isn't). If you square both sides, you get: x2 = 25 which also has the solution x = 5. However, it also has the extraneous solution x = -5, which is not a solution to the original equation.
What must you do to determine weather a soluion is an exraneous solution?
If the solution, makes the denominator equal to zero, makes the expression of a logarithm or under a square root, a negative one. If there are more than one denominator, check all the solutions. Usually, we determine the extraneous solutions before we solve the equation.
How do you solve a square root equation?
To solve a square root equation, first isolate the square root term on one side of the equation. Then, square both sides to eliminate the square root. After squaring, solve the resulting equation for the variable. Finally, check your solutions to ensure they are valid, as squaring can introduce extraneous solutions.
What is another word for not needed?
extraneous " not pertinent; irrelevant: an extraneous remark; extraneous decoration."
A sentence with the word extraneous?
During the long, boring lecture, most people agreed that much of the information was extraneous.
What is the definition of extraneous?
Extraneous means 'coming from the outside'.
What is a extraneous solution?
A solution to an equation that you get at the end of whatever method you use that does not actually solve the original equation. One well-known example:1=2 ====>0=0 Therefore, one equals two.x0 x0The laws of algebra says that we can do this because we multiplied both sides by zero. Logically, we all know this isn't actually true. This is what extraneous solutions look like when solving linear equations:2x+3=9 If you assume x=1... 2(1)+3=9 ...and multiply everything by 0...0=0. Therefore, my guess is correct and x=1.
How is an extraneous solution of a ration equation similar to an excluded value of a rational equation?
An extraneous solution of a rational equation is a solution that emerges from the algebraic process but does not satisfy the original equation, while an excluded value is a value that makes the denominator zero and is therefore not permissible in the equation. Both concepts highlight the limitations and constraints of rational expressions. Excluded values can lead to extraneous solutions if they are mistakenly included in the solution set. Thus, both are essential to consider when solving rational equations to ensure valid solutions.
What do you call the solution of a equation derived from an original equation that is not a solution of the original equation?
That's an extraneous solution. You need to check for these when algebraically solving equations, especially when you take both sides of an equation to a power.
