answersLogoWhite

0


Want this question answered?

Be notified when an answer is posted

Add your answer:

Earn +20 pts
Q: When do you need to check for extraneous solutions?
Write your answer...
Submit
Still have questions?
magnify glass
imp
Related questions

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.


What is another word for not needed?

extraneous " not pertinent; irrelevant: an extraneous remark; extraneous decoration."


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.


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 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.


What reasoning and explanations can be used when solving radical equations?

The basic method is the same as for other types of equations: you need to isolate the variable ("x", or whatever variable you need to solve for). In the case of radical equations, it often helps to square both sides of the equation, to get rid of the radical. You may need to rearrange the equation before squaring. It is important to note that when you do this (square both sides), the new equation may have solutions which are NOT part of the original equation. Such solutions are known as "extraneous" solutions. Here is a simple example (without radicals): x = 5 (has one solution, namely, 5) Squaring both sides: x squared = 25 (has two solutions, namely 5, and -5). To protect against this situation, make sure you check each "solution" of the modified equation against the original equation, and reject the solutions that don't satisfy it.


How do you use the word extraneous in a sentence?

The crowd's not entirely silent, but there's not too much extraneous talking.