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Emily778

  • 2 years ago

check for extraneous solutions. sqrt x+7-x=1 Please show step by step on how to do this. Thankyou.

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  1. RolyPoly
    • 2 years ago
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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?

  2. Emily778
    • 2 years ago
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    Wat?

  3. Emily778
    • 2 years ago
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    @Krazete

  4. Emily778
    • 2 years ago
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    I don't get the way you're explaining it to me @RolyPoly

  5. Krazete
    • 2 years ago
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    Please make use of parentheses. The way you write problems is sorta confusing. Is it √(x+7)-x=1 or ...?

  6. Emily778
    • 2 years ago
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    I guess. Sorry, it doesn't show parentheses on my math problem.

  7. RolyPoly
    • 2 years ago
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    Is the equation (1)\(\sqrt{ x+7-x} =1\) or (2) \(\sqrt{x}+7-x=1\)?

  8. Emily778
    • 2 years ago
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    nvm, i got the answer. Thx

  9. Emily778
    • 2 years ago
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    nvm.. I tried wolframalpha. But only get two step by steps each day:(

  10. Emily778
    • 2 years ago
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    I'll have to get the answer tomorrow.

  11. RolyPoly
    • 2 years ago
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    It would be better if you know how to solve it, instead of just relying on WolframAlpha.

  12. Emily778
    • 2 years ago
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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.

  13. Emily778
    • 2 years ago
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    Honestly, I just need credits/passed classes

  14. Emily778
    • 2 years ago
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    you can argue all you want, but it's true.

  15. RolyPoly
    • 2 years ago
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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 :)

  16. Emily778
    • 2 years ago
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    can you just show me please? I'm 18 lessons behind:(

  17. nikato
    • 2 years ago
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    \[\sqrt{x+7}-x=1\]

  18. nikato
    • 2 years ago
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    add x to both sides

  19. Emily778
    • 2 years ago
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    It would be a different story if I wasn't that behind

  20. RolyPoly
    • 2 years ago
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    \[\sqrt{x-7-x}=1\]\[\sqrt{x-7}-x=1\]\[\sqrt{x}-7-x=1\] Which one is your question?

  21. Emily778
    • 2 years ago
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    like this @nikato |dw:1388896983931:dw|

  22. Emily778
    • 2 years ago
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    the 2nd one @RolyPoly

  23. nikato
    • 2 years ago
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    yup

  24. Emily778
    • 2 years ago
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    what next?

  25. nikato
    • 2 years ago
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    so now u have|dw:1388897108757:dw| now square both sides

  26. Emily778
    • 2 years ago
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    i know 9 is the solution

  27. Emily778
    • 2 years ago
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    what next?

  28. nikato
    • 2 years ago
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    did u square both sides. and simplified it?

  29. Emily778
    • 2 years ago
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    how do I simplify it?

  30. nikato
    • 2 years ago
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    |dw:1388897450469:dw|does that make sense?

  31. Emily778
    • 2 years ago
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    yeah.

  32. Emily778
    • 2 years ago
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    what next?

  33. nikato
    • 2 years ago
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    subtract x and 7 on both sides so that the equation equal 0

  34. nikato
    • 2 years ago
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    |dw:1388897691356:dw|

  35. Emily778
    • 2 years ago
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    what next? :D ha

  36. nikato
    • 2 years ago
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    |dw:1388897800670:dw| can u factor the right side?

  37. Emily778
    • 2 years ago
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    can you show me? eheh

  38. nikato
    • 2 years ago
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    |dw:1388898386363:dw|

  39. Emily778
    • 2 years ago
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    9?

  40. Emily778
    • 2 years ago
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    @nikato

  41. Emily778
    • 2 years ago
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    it has to be 9.

  42. nikato
    • 2 years ago
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    no, i dont think 9 is a solution. try pluggin it back into the origianl equation. it doesnt work

  43. nikato
    • 2 years ago
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    |dw:1388899069611:dw|

  44. Emily778
    • 2 years ago
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    then you did it wrong. Ugh. Wolfram said it was 9

  45. nikato
    • 2 years ago
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    no, im for sure 9 is not an answer. it doesnt make sense. its one fo those^

  46. Emily778
    • 2 years ago
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    @Krazete is he wrong or not?

  47. Emily778
    • 2 years ago
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    sorry, nikato. I gotta make sure.

  48. nikato
    • 2 years ago
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    yea, its fine. whatever u feel is right

  49. Krazete
    • 2 years ago
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    nikato's right.

  50. Emily778
    • 2 years ago
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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.

  51. nikato
    • 2 years ago
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    maybe u typed in the wrong equation in wolfrma

  52. Krazete
    • 2 years ago
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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.

  53. Emily778
    • 2 years ago
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    nikato, what do I do next? Sorry for doubting you

  54. nikato
    • 2 years ago
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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

  55. Emily778
    • 2 years ago
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    one of them is 2.

  56. nikato
    • 2 years ago
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    yes. and the other?

  57. Emily778
    • 2 years ago
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    o?

  58. nikato
    • 2 years ago
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    no, -3. so now u want to find if there is anyextraneous answers

  59. nikato
    • 2 years ago
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    plug both back into the equation and see if they make sense|dw:1388900195738:dw|

  60. Emily778
    • 2 years ago
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    ugh. How much more is there??

  61. Emily778
    • 2 years ago
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    what next?

  62. nikato
    • 2 years ago
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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

  63. Emily778
    • 2 years ago
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    it's 1.

  64. Emily778
    • 2 years ago
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    thanks. :p

  65. nikato
    • 2 years ago
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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

  66. Emily778
    • 2 years ago
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    I did it in my calculator. How'd you get your answer?

  67. nikato
    • 2 years ago
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    no, thats not what i meant

  68. nikato
    • 2 years ago
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    |dw:1388901004098:dw|

  69. Emily778
    • 2 years ago
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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.

  70. nikato
    • 2 years ago
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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

  71. Emily778
    • 2 years ago
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    so what is the answer???

  72. nikato
    • 2 years ago
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    just 2

  73. nikato
    • 2 years ago
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    becuz like i said ^ -3 is an extraneous solution

  74. Emily778
    • 2 years ago
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    so, I would put "x=2 only"?

  75. nikato
    • 2 years ago
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    yup

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