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anonymous

  • one year ago

PLEASE HELP NOT QUITE SURE ON THIS QUESTION Given the equation −4Square root of x minus 3 = 12, solve for x and identify if it is an extraneous solution.

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  1. anonymous
    • one year ago
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    this is the equation: \[\sqrt[-4]{x-3} = 12\]

  2. Nnesha
    • one year ago
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    \[\huge\rm -4\sqrt{x-3}=12\] first move the -4 to the right side

  3. Nnesha
    • one year ago
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    it's not 4th root right ? is it -4 (sqrt{x-3} ??

  4. anonymous
    • one year ago
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    yes you have it right

  5. anonymous
    • one year ago
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    @Nnesha @imqwerty

  6. Nnesha
    • one year ago
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    okay then first move the -4 to the right side how would do that ? divide , multiply add , or subtract ?

  7. anonymous
    • one year ago
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    you would add

  8. anonymous
    • one year ago
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    @Nnesha

  9. Nnesha
    • one year ago
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    now it's -4 times sqrt{x-3} what is opposite of multiplication ?

  10. anonymous
    • one year ago
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    division

  11. Nnesha
    • one year ago
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    yes right so divide both side by -4

  12. anonymous
    • one year ago
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    x-3=-2?

  13. Nnesha
    • one year ago
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    12/-4 = ??

  14. anonymous
    • one year ago
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    -3

  15. Nnesha
    • one year ago
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    \[\sqrt{x-3}=-3\] now take square both sides to cancel out the square root

  16. anonymous
    • one year ago
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    so it would be 0

  17. Nnesha
    • one year ago
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    how ??

  18. anonymous
    • one year ago
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    wait no -9

  19. anonymous
    • one year ago
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    sorry

  20. anonymous
    • one year ago
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    x-3=-9

  21. Nnesha
    • one year ago
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    \[\huge\rm (\sqrt{x-3})^2=(-3)^2\] when you take even power of NEGATIVE you will ALAWAYS get positive answer

  22. anonymous
    • one year ago
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    oh okay

  23. Nnesha
    • one year ago
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    sp (-3)^2 =? it's same as -3 times -3

  24. anonymous
    • one year ago
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    positive 9

  25. Nnesha
    • one year ago
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    x-3= 9 solve for x

  26. anonymous
    • one year ago
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    and then you would add 3 to get positive 12

  27. anonymous
    • one year ago
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    and then would it be extraneous or not extraneous?

  28. Nnesha
    • one year ago
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    okay to check if it's extraneous or not substitute x for 12 in the original equation

  29. Nnesha
    • one year ago
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    if both sides are equal then 12 isn't extraneous

  30. anonymous
    • one year ago
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    both sides came out equal so its not extraneous

  31. Nnesha
    • one year ago
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    how did you get equal sides ?

  32. anonymous
    • one year ago
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    honestly i don't know

  33. Nnesha
    • one year ago
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    \[-4\sqrt{12-3}=12\] now solve

  34. Nnesha
    • one year ago
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    show me how did you do it ?

  35. anonymous
    • one year ago
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    ok

  36. anonymous
    • one year ago
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    im not sure how i did it but could you show me how to do it the right way please?

  37. anonymous
    • one year ago
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    i just guessed because i wasn't sure how to do it, the 4 on the outside of the sqr root confuses me

  38. Nnesha
    • one year ago
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    okay so we replaced x with 12 right now solve \[-4\sqrt{12-3}=12\] 12-3 and then take square root

  39. Nnesha
    • one year ago
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    seee i knew it remember it's not 4 it's -4

  40. Nnesha
    • one year ago
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    hint: \[-1\cancel{=}1\]

  41. anonymous
    • one year ago
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    i got \[\sqrt[16]{9} =12\]

  42. anonymous
    • one year ago
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    that 16 isnt an exponent

  43. Nnesha
    • one year ago
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    hmm how did you get 16? 12-3 = ??

  44. anonymous
    • one year ago
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    i did -4^2

  45. Nnesha
    • one year ago
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    don't take square \[-4\sqrt{12-3}\] you should substitute x for 12 into the original equation

  46. Nnesha
    • one year ago
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    12-3= 9 right \[-4\sqrt{9}\] now solve

  47. anonymous
    • one year ago
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    equals -12

  48. Nnesha
    • one year ago
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    yes so -12 =12 ?

  49. anonymous
    • one year ago
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    sorry as you can tell i struggle with algebra

  50. anonymous
    • one year ago
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    no so they are extraneous

  51. anonymous
    • one year ago
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    the solution is not extraneous

  52. anonymous
    • one year ago
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    solution is extraneous right ? @Nnesha

  53. Nnesha
    • one year ago
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    which one is it extraneous or not ? like i said if you get equal sides THEN 12 is not extraneous

  54. Nnesha
    • one year ago
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    -12=12 both sides are equal ?

  55. anonymous
    • one year ago
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    no they are not equal so it is extraneous

  56. Nnesha
    • one year ago
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    yes right

  57. anonymous
    • one year ago
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    thanks so much for all your help that took awhile but thank you

  58. Nnesha
    • one year ago
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    my pleasure. :=)

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