Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

mukushla

  • 2 years ago

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

  • This Question is Closed
  1. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    f(x)=2 and 1

  2. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    how?

  3. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @nipunmalhotra93 @sauravshakya post complete solution ... i'll check it later

  4. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Take it to the form a^3+b^3

  5. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1347716779899:dw|

  6. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Wll that be enough

  7. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    So, f(x) can only be either 1 or 2

  8. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    So the hard part is to find x

  9. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Was that correct @mukushla

  10. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    x=2

  11. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    thats correct...complete it :) can u find the exact range of f(x) ?

  12. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1347720322437:dw|

  13. nipunmalhotra93
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    well, here's my solution. |dw:1347734655828:dw||dw:1347734803553:dw|

  14. nipunmalhotra93
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1347736319687:dw|

  15. nipunmalhotra93
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1347736404280:dw|

  16. nipunmalhotra93
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so three answers in total.... :)

  17. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Fantastic work @nipunmalhotra93 :)

  18. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i think the answer is only x=2

  19. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1347769714174:dw|

  20. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    I think that also works

  21. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    that gives f(x)=1 ?

  22. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    YEP

  23. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    And is solved the equation

  24. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    emm... http://www.wolframalpha.com/input/?i=%5Csqrt%5B3%5D%7Bx-1%7D%2B%5Csqrt%5B3%5D%7B3-x%7D%3D1

  25. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    WHAT! so my solution was wrong

  26. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    because the range of that function is\[[\sqrt[3]{2},2]\]

  27. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Cant it be zero as x---->infinity

  28. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Oh I got it there is a problem with my solution

  29. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    So if (x)^1/2 + y^1/2 =2........i and x^1/2 - y^1/2 =4.......ii

  30. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    It has no solution........ though we get the value of x and y..... if we solve those equation

  31. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Same thing happened to my equations

  32. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    right? @mukushla

  33. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    where that equations come from?

  34. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    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

  35. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Solved those two equations

  36. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Let x-1=A and x-3=B

  37. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Square first equation

  38. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1347770764883:dw|

  39. nipunmalhotra93
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @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

  40. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yeah thats right...have u checked ur solutions?

  41. nipunmalhotra93
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yup! when I plug in x=.98165, calculate cube root of 1-x and then put a minus sign with it. That works fine.

  42. nipunmalhotra93
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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.

  43. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    @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

  44. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    @mukushla can u PLZ CHECK it

  45. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    I think the range of f(x) is|dw:1347775870157:dw|

  46. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    thats right :)

  47. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    good job saura :)

  48. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    But I still have a question for u

  49. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    guys @sauravshakya @nipunmalhotra93 u cooked the problem :D

  50. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yeah what ?

  51. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    (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

  52. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    There I solved for x and got the value

  53. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Similarly if I solved this (x)^1/2 + y^1/2 =2........i and x^1/2 - y^1/2 =4.......ii

  54. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Will I get the values of x and y

  55. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    sorry can u plz elaborate ? where these 2 equations come from?

  56. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    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

  57. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    this one

  58. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no second

  59. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Second one just came from my mind

  60. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ahh ok

  61. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    While I gave a thought when u said that x=2 only

  62. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    nope there is no answer for that system

  63. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    that gives\[\sqrt{y}=-1\]

  64. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Yep

  65. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    So, Actually my approach was not really good............ As it may give somrtime solution when there should be no solution

  66. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yeah maybe :)

  67. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok i really enjoyed guys....thank u

  68. sauravshakya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Welcome........ And thanx for such a nice question

  69. nipunmalhotra93
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @sauravshakya haha yea we both had the same answer :D @mukushla I enjoyed it too man... thanks !!

  70. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.