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mukushla Group Title

ok this is mine \[f(x)=\sqrt[3]{x-1}+\sqrt[3]{3-x}\]find all \(x \in \mathbb{R}\) such that \(f(x) \in \mathbb{N}\)

  • one year ago
  • one year ago

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  1. sauravshakya Group Title
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    f(x)=2 and 1

    • one year ago
  2. mukushla Group Title
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    how?

    • one year ago
  3. mukushla Group Title
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    @nipunmalhotra93 @sauravshakya post complete solution ... i'll check it later

    • one year ago
  4. sauravshakya Group Title
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    Take it to the form a^3+b^3

    • one year ago
  5. sauravshakya Group Title
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    |dw:1347716779899:dw|

    • one year ago
  6. sauravshakya Group Title
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    Wll that be enough

    • one year ago
  7. sauravshakya Group Title
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    So, f(x) can only be either 1 or 2

    • one year ago
  8. sauravshakya Group Title
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    So the hard part is to find x

    • one year ago
  9. sauravshakya Group Title
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    Was that correct @mukushla

    • one year ago
  10. sauravshakya Group Title
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    x=2

    • one year ago
  11. mukushla Group Title
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    thats correct...complete it :) can u find the exact range of f(x) ?

    • one year ago
  12. sauravshakya Group Title
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    |dw:1347720322437:dw|

    • one year ago
  13. nipunmalhotra93 Group Title
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    well, here's my solution. |dw:1347734655828:dw||dw:1347734803553:dw|

    • one year ago
  14. nipunmalhotra93 Group Title
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    |dw:1347736319687:dw|

    • one year ago
  15. nipunmalhotra93 Group Title
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    |dw:1347736404280:dw|

    • one year ago
  16. nipunmalhotra93 Group Title
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    so three answers in total.... :)

    • one year ago
  17. mukushla Group Title
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    Fantastic work @nipunmalhotra93 :)

    • one year ago
  18. mukushla Group Title
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    i think the answer is only x=2

    • one year ago
  19. sauravshakya Group Title
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    |dw:1347769714174:dw|

    • one year ago
  20. sauravshakya Group Title
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    I think that also works

    • one year ago
  21. mukushla Group Title
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    that gives f(x)=1 ?

    • one year ago
  22. sauravshakya Group Title
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    YEP

    • one year ago
  23. sauravshakya Group Title
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    And is solved the equation

    • one year ago
  24. mukushla Group Title
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    emm... http://www.wolframalpha.com/input/?i=%5Csqrt%5B3%5D%7Bx-1%7D%2B%5Csqrt%5B3%5D%7B3-x%7D%3D1

    • one year ago
  25. sauravshakya Group Title
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    WHAT! so my solution was wrong

    • one year ago
  26. mukushla Group Title
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    because the range of that function is\[[\sqrt[3]{2},2]\]

    • one year ago
  27. sauravshakya Group Title
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    Cant it be zero as x---->infinity

    • one year ago
  28. sauravshakya Group Title
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    Oh I got it there is a problem with my solution

    • one year ago
  29. sauravshakya Group Title
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    So if (x)^1/2 + y^1/2 =2........i and x^1/2 - y^1/2 =4.......ii

    • one year ago
  30. sauravshakya Group Title
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    It has no solution........ though we get the value of x and y..... if we solve those equation

    • one year ago
  31. sauravshakya Group Title
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    Same thing happened to my equations

    • one year ago
  32. sauravshakya Group Title
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    right? @mukushla

    • one year ago
  33. mukushla Group Title
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    where that equations come from?

    • one year ago
  34. sauravshakya Group Title
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    Actually the equations I got was: (x-1)^1/3 - (x-3)^1/3 =1...........i (x-1)^2/3 +{(x-1)(x-3)}^1/3 + (x-3)^2/3=2........ii

    • one year ago
  35. sauravshakya Group Title
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    Solved those two equations

    • one year ago
  36. sauravshakya Group Title
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    Let x-1=A and x-3=B

    • one year ago
  37. sauravshakya Group Title
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    Square first equation

    • one year ago
  38. sauravshakya Group Title
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    |dw:1347770764883:dw|

    • one year ago
  39. nipunmalhotra93 Group Title
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    @mukushla actually I think that wolfram uses the domain of \[\sqrt[3]{x}\]to be only non negative real nos. I have noticed that it gives complex answers when we try to plug in negative reals in the cube root function http://www.wolframalpha.com/input/?i=%5Csqrt%5B3%5D%7B-1%7D

    • one year ago
  40. mukushla Group Title
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    yeah thats right...have u checked ur solutions?

    • one year ago
  41. nipunmalhotra93 Group Title
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    yup! when I plug in x=.98165, calculate cube root of 1-x and then put a minus sign with it. That works fine.

    • one year ago
  42. nipunmalhotra93 Group Title
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    similarly, when I put x=3.0183 , I calculate x-3 and put minus sig with the cube root of x-3 to get \[\sqrt[3]{3-x}\] That's the only possible way to check it I think.

    • one year ago
  43. sauravshakya Group Title
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    @nipunmalhotra93 Actually u and I got the same answers....|dw:1347775568533:dw| But And the substituted the value |dw:1347775753579:dw| in f(x) I got 1

    • one year ago
  44. sauravshakya Group Title
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    @mukushla can u PLZ CHECK it

    • one year ago
  45. sauravshakya Group Title
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    I think the range of f(x) is|dw:1347775870157:dw|

    • one year ago
  46. mukushla Group Title
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    thats right :)

    • one year ago
  47. mukushla Group Title
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    good job saura :)

    • one year ago
  48. sauravshakya Group Title
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    But I still have a question for u

    • one year ago
  49. mukushla Group Title
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    guys @sauravshakya @nipunmalhotra93 u cooked the problem :D

    • one year ago
  50. mukushla Group Title
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    yeah what ?

    • one year ago
  51. sauravshakya Group Title
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    (x-1)^1/3 - (x-3)^1/3 =1...........i (x-1)^2/3 +{(x-1)(x-3)}^1/3 + (x-3)^2/3=2........ii

    • one year ago
  52. sauravshakya Group Title
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    There I solved for x and got the value

    • one year ago
  53. sauravshakya Group Title
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    Similarly if I solved this (x)^1/2 + y^1/2 =2........i and x^1/2 - y^1/2 =4.......ii

    • one year ago
  54. sauravshakya Group Title
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    Will I get the values of x and y

    • one year ago
  55. mukushla Group Title
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    sorry can u plz elaborate ? where these 2 equations come from?

    • one year ago
  56. sauravshakya Group Title
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    Which one: (x-1)^1/3 - (x-3)^1/3 =1...........i (x-1)^2/3 +{(x-1)(x-3)}^1/3 + (x-3)^2/3=2........ii

    • one year ago
  57. sauravshakya Group Title
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    this one

    • one year ago
  58. mukushla Group Title
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    no second

    • one year ago
  59. sauravshakya Group Title
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    Second one just came from my mind

    • one year ago
  60. mukushla Group Title
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    ahh ok

    • one year ago
  61. sauravshakya Group Title
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    While I gave a thought when u said that x=2 only

    • one year ago
  62. mukushla Group Title
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    nope there is no answer for that system

    • one year ago
  63. mukushla Group Title
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    that gives\[\sqrt{y}=-1\]

    • one year ago
  64. sauravshakya Group Title
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    Yep

    • one year ago
  65. sauravshakya Group Title
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    So, Actually my approach was not really good............ As it may give somrtime solution when there should be no solution

    • one year ago
  66. mukushla Group Title
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    yeah maybe :)

    • one year ago
  67. mukushla Group Title
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    ok i really enjoyed guys....thank u

    • one year ago
  68. sauravshakya Group Title
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    Welcome........ And thanx for such a nice question

    • one year ago
  69. nipunmalhotra93 Group Title
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    @sauravshakya haha yea we both had the same answer :D @mukushla I enjoyed it too man... thanks !!

    • one year ago
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