Emily778
check for extraneous solutions.
sqrt x+7-x=1
Please show step by step on how to do this. Thankyou.
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RolyPoly
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Let \(u=\sqrt{x}\), then x = \(u^2\)
Now, the equation becomes
\[u+7-u^2=1\]
Can you do it?
Emily778
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Wat?
Emily778
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@Krazete
Emily778
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I don't get the way you're explaining it to me @RolyPoly
Krazete
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Please make use of parentheses. The way you write problems is sorta confusing.
Is it √(x+7)-x=1 or ...?
Emily778
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I guess. Sorry, it doesn't show parentheses on my math problem.
RolyPoly
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Is the equation (1)\(\sqrt{ x+7-x} =1\) or (2) \(\sqrt{x}+7-x=1\)?
Emily778
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nvm, i got the answer. Thx
Emily778
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nvm.. I tried wolframalpha. But only get two step by steps each day:(
Emily778
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I'll have to get the answer tomorrow.
RolyPoly
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It would be better if you know how to solve it, instead of just relying on WolframAlpha.
Emily778
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eh, true. But lets be honest with ourselves, I'm never going to use this advanced of math in the future.
Emily778
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Honestly, I just need credits/passed classes
Emily778
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you can argue all you want, but it's true.
RolyPoly
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Don't want to argue, just want to help you pass the course and you can learn how to solve it at the same time :)
Emily778
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can you just show me please? I'm 18 lessons behind:(
nikato
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\[\sqrt{x+7}-x=1\]
nikato
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add x to both sides
Emily778
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It would be a different story if I wasn't that behind
RolyPoly
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\[\sqrt{x-7-x}=1\]\[\sqrt{x-7}-x=1\]\[\sqrt{x}-7-x=1\]
Which one is your question?
Emily778
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like this @nikato |dw:1388896983931:dw|
Emily778
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the 2nd one @RolyPoly
nikato
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yup
Emily778
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what next?
nikato
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so now u have|dw:1388897108757:dw| now square both sides
Emily778
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i know 9 is the solution
Emily778
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what next?
nikato
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did u square both sides. and simplified it?
Emily778
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how do I simplify it?
nikato
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|dw:1388897450469:dw|does that make sense?
Emily778
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yeah.
Emily778
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what next?
nikato
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subtract x and 7 on both sides so that the equation equal 0
nikato
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|dw:1388897691356:dw|
Emily778
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what next? :D ha
nikato
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|dw:1388897800670:dw| can u factor the right side?
Emily778
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can you show me? eheh
nikato
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|dw:1388898386363:dw|
Emily778
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9?
Emily778
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@nikato
Emily778
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it has to be 9.
nikato
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no, i dont think 9 is a solution. try pluggin it back into the origianl equation. it doesnt work
nikato
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|dw:1388899069611:dw|
Emily778
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then you did it wrong. Ugh. Wolfram said it was 9
nikato
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no, im for sure 9 is not an answer. it doesnt make sense. its one fo those^
Emily778
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@Krazete is he wrong or not?
Emily778
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sorry, nikato. I gotta make sure.
nikato
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yea, its fine. whatever u feel is right
Krazete
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nikato's right.
Emily778
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okayy,, it's just wolfram said the solution was 9. But I guess it's better to have something than nothing at all.
nikato
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maybe u typed in the wrong equation in wolfrma
Krazete
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Look at what Wolfram says under "input." Is it the same as your problem? It might've calculated √x instead of √(x+7). Parentheses are quite important.
Emily778
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nikato, what do I do next? Sorry for doubting you
nikato
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|dw:1388899779946:dw| solve for x. did most of the work. should be easy for u. there are suppose to be 2 answers
Emily778
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one of them is 2.
nikato
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yes. and the other?
Emily778
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o?
nikato
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no, -3. so now u want to find if there is anyextraneous answers
nikato
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plug both back into the equation and see if they make sense|dw:1388900195738:dw|
Emily778
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ugh. How much more is there??
Emily778
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what next?
nikato
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no, this is it. check if both of those equation are true. if they are not, then that "x" is extraneous
Emily778
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it's 1.
Emily778
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thanks. :p
nikato
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WAIT NO. its either 2 or -3. i helped plug in both in for x
the first one is x=2
and the other is x=-3
Emily778
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I did it in my calculator. How'd you get your answer?
nikato
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no, thats not what i meant
nikato
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|dw:1388901004098:dw|
Emily778
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I'm sorry, I still don't get how you got those answers. I got -5 and 1. 1 was correct. -5 was incorrect.
nikato
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yes. so that means -3 is the extraneous answer.
remember how we worked the problem, and got 2 and -3 as the naswer.
however when u plug -3 back into the original equation u get -5 instead of 1. which means the answer doesnt "work" which we call an extraneous answer
Emily778
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so what is the answer???
nikato
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just 2
nikato
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becuz like i said ^ -3 is an extraneous solution
Emily778
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so, I would put "x=2 only"?
nikato
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yup