1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Maximum value(Tricky)

  1. Jul 13, 2008 #1
    1. The problem statement, all variables and given/known data
    If x belongs set of real numbers, find the maximum value of [tex]2(a-x)(x+\sqrt{x^{2}+b^{2}})[/tex]

    3. The attempt at a solution
    All that I could do was to try and diffrentiate the above expression but it yields a polynomial of degree 4. A hint to this question is that it belongs to the Quadratic Equations Chapter. And the answer to th above question is [tex]a^{2}+b^{2}[/tex]
    Please help me. I cant make head or tail out of it.
     
  2. jcsd
  3. Jul 13, 2008 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    complete the square …

    Hi ritwik06! :smile:

    You have to complete the square (twice).

    Hint: start with the easy bit … the 2ax. :smile:
     
  4. Jul 13, 2008 #3
    Re: complete the square …

    I didnt get u tim. Coul u please be more explicit...
    thanks
     
  5. Jul 13, 2008 #4

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Re: complete the square …

    Do you know what "complete the square" means?

    If you do … then try it! :smile:

    (If you don't, I'll show you an example.)
     
  6. Jul 13, 2008 #5
    Re: complete the square …

    I tried this:
    help me!!!
    [tex]b^{2}+2ax+2a(\sqrt{b^{2}+x^{2}})-(x+(\sqrt{b^{2}+x^{2}))^{2}[/tex]
    Hey, please help. Dont think that I havnt tried it at all. I have done all that I could. Thanks for the help.
     
  7. Jul 13, 2008 #6

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Re: complete the square …

    ok … two hints:

    i] You have two squares to complete, and you need x2 in both of them … so you'll have to split up the -2x2, won't you? :wink:

    ii] You know what the answer is, so that gives you a pretty good clue as to what might be left over! :smile:

    (And, as I said, get rid of the 2ax first.)
     
  8. Jul 14, 2008 #7
    Re: complete the square …

    I have worked more on this problem but yet no results come my way;
    [tex]((a+\sqrt(x^{2}+b^{2}))^{2})-((x-a)^{2})-((x+\sqrt(x^{2}+b^{2}))^{2})[/tex]
     
  9. Jul 14, 2008 #8

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Re: complete the square …

    ok …

    try [tex]2(a-x)(x+\sqrt{x^{2}+b^{2}}) = a^2\ -\ (a-x)^2\ -\ x^2\ +\ 2(a-x)\sqrt{x^{2}+b^{2}}[/tex] :smile:
     
  10. Jul 21, 2008 #9

    Borek

    User Avatar

    Staff: Mentor

    It is not a correct answer.

    But I must admit I have no idea how to complete these squares. Not that I am surprised, I am mathematically challenged. I have solved it by brute force, which was much easier then expected.
     
  11. Jul 21, 2008 #10

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    completing the square

    Hi Borek! :smile:

    Try adding [itex]b^2\ -\ b^2[/itex] to my last post. :smile:
     
  12. Jul 22, 2008 #11

    Borek

    User Avatar

    Staff: Mentor

    Arrgh. There is nothing like solving different question that was asked. I was looking for x such that the function given gets maximum value. That's for

    [tex]x = \frac {a^2-b^2} {2a}[/tex]

    but

    [tex]{a^2+b^2}[/tex]

    is a correct max value.

    Thanks TT :smile:
     
  13. Jul 24, 2008 #12
    Thanks a lot Tim.
    I had got my answer the day you had posted your second last reply.
    Thank you very very much. I am sorry for xpressing my gratitude a bit late. Thanks again.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Maximum value(Tricky)
  1. Fimd the maximum value (Replies: 6)

  2. Maximum value of a_n (Replies: 29)

  3. Finding maximum value (Replies: 21)

  4. Finding maximum value (Replies: 9)

Loading...