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Mertsj
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The deal is this....when you square an equation you sometimes end up with a "solution" that doesn't make the sentence true. Those are called extraneous roots. They are the reason your teacher tells you to always check the answers you get when solving radical equations. Sometimes they don't work. Let me show you an example.
Mertsj
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|dw:1366677654241:dw|
precal
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also, the domain helps in identifying extraneous solutions
Mertsj
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And that answer will not check. It is an extraneous solution.
sugarheart
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I got it, it's 5
Mertsj
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You solved your problem?
sugarheart
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Yes
Mertsj
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Good for you!!!
Mertsj
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Hey...just a minute. I don't think 5 will check.
Mertsj
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|dw:1366677868347:dw|
Mertsj
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Some graduate student made a grievous error in writing your question.
sugarheart
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What?
Mertsj
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As you can see...5 does not make the sentence true.
Mertsj
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So if 5 was accepted as a correct answer, someone has put the wrong answer into the computer program .
Mertsj
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Didn't you also get -3 as an answer?
precal
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you mean |dw:1366678251238:dw|
sugarheart
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@precal Why does that matter though.. It wasn't my question it was his example
Mertsj
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|dw:1366678291957:dw|
precal
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because 13 is extraneous
Mertsj
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You see...-3 is actually an answer. It checks. 5 is extraneous.
Mertsj
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@precal That was an example I constructed to illustrate extraneous roots for the asker
precal
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sorry Mertsj, saw your example and not the actual problem
Mertsj
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np
precal
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Key idea @sugarheart is that when solving solutions for square root equations or radicals, extraneous solutions do exist so we have to check for them
sugarheart
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5 is the extraneous solution and that's why it's was the answer to my problem
Mertsj
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oh. So they were asking for the extraneous root. Cool. Then it is right.
sugarheart
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Yes lol
Mertsj
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Yep. I reread the question. Always helps to know the question one is attempting to answer.
precal
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extraneous solutions can also, occur in other functions (example logarithmic)