Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

mukushla Group Title

dont need weird mathematics :) \[f(x)=\sqrt{x^2-2x+10}-\sqrt{x^2-2x+2}\] find all \(x \in \mathbb{R}\) such that \(f(x) \in \mathbb{N}\)

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. mukushla Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    @sauravshakya @ganeshie8 @eliassaab @TuringTest

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

    x=1,\[\frac{ -1-\sqrt{5} }{2 }\], \[\frac{-1+\sqrt{5} }{2 }\]

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

    is that it?

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

    let me check it :)

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

    u are close :) but dont tell the answer plz...so others can think on that :)

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

    Ok fine. Thanks :)

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

    So only when x=1 or are there any other value..... I think yes because irrational-irrational can be integer

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

    some other values...

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

    I mean are there any other values of x

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

    yeah there are.

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

    dont post ur solution :) just values of x

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

    Ok

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

    So I delete it and send u msg for the vaues of x

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

    no give the values of x here :)

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

    |dw:1347712962196:dw|

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

    oh crap! I misread x^2 as x^3 :\

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

    So was my answer correct @nipunmalhotra93

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

    @mukushla can u PLZ CHECK MY ANSWER

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

    completely right :)

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

    so i think nipun got it also :)

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

    Actually f(x)=2 and 1

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

    yup

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

    GREAT QUESTION

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

    Took me a lot to do this......

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

    :D the font is too small I thought it was x^3 lol :D

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

    everyone is one here...lol

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

    @mukushla CAN U PLZ GIVE SOME QUESTION LIKE THIS PLZ.......

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

    of course

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

    GREAT

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

    @sauravshakya I'd like to know your approach. Would you mind telling it? This is how I got it. \[\sqrt{p+10}-\sqrt{p+2}=A\] A is natural so, \[p+10=A ^{2}+p+2+2A \sqrt{p+2}\] \[10-A^2-2=2A \sqrt{p+2}\] so, \[\frac{ 4}{A }-\frac{ A }{ 2 }=\sqrt{p+2}\] So, A can only be 1 or 2 (as A is natural) for \[\sqrt{p+2}\] to be real. Put p=x^2-2x and solving \[\sqrt{p+2}=1 or \sqrt{p+2}=7/2\] , we get the answer. This is a good question that's why I wanna know your method. :)

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

    Rationalize and u will get|dw:1347715001113:dw|

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

    Right?

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

    \[f(x)=\sqrt{x^2-2x+10}-\sqrt{x^2-2x+2}=\frac{8}{\sqrt{x^2-2x+10}+\sqrt{x^2-2x+2}}\]\[f(x)=\frac{8}{\sqrt{(x-1)^2+9}+\sqrt{(x-1)^2+1}}\le\frac{8}{\sqrt{9}+\sqrt{1}}=2\]so f(x)=1 or 2 same as saura's method

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

    That will make it easy to solve

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

    opps. Now, when f(x)=1 (x^2-2x+10)^1/2 - (x^2-2x+2)^1/2=1........i (x^2-2x+10)^1/2 + (x^2-2x+2)^1/2=8........ii

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

    So, 2*(x^2-2x+10)^1/2=9

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

    now, solve for x

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

    thats it

    • 2 years ago
    • Attachments:

See more questions >>>

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.