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Homework Help: Solving the equation

  1. Jul 4, 2013 #1
    1. The problem statement, all variables and given/known data
    Find all real numbers ##x## such that,

    2. Relevant equations

    3. The attempt at a solution
    Moving the second term on LHS to the right and squaring both the sides,
    Squaring again leads to terms containing 4th and 3rd power of x and I don't find a way to proceed further. Here's the expression I get after squaring and rearranging,

    Any help is appreciated. Thanks!
  2. jcsd
  3. Jul 4, 2013 #2


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  4. Jul 4, 2013 #3

    Multiply both sides by [itex]\left(x-\frac{1}{x}\right)^{1/2}-\left(1-\frac{1}{x}\right)^{1/2}[/itex] to get

    Now, add the two equations to get:


    Let [itex]y=\sqrt{\left(x-\frac{1}{x}\right)}[/itex]

    Then [tex]y^2-2y+1=0[/tex]
  5. Jul 5, 2013 #4
    That was too obvious to be missed. :tongue:

    Thank you! :smile:
    Nice one Chet, thanks a lot! :smile:
  6. Jul 5, 2013 #5

    Your final equation is incorrect. You need to redo the squaring and rearranging. The correct relationship is:
    This is the same as:
  7. Jul 5, 2013 #6
    Sorry about the typo, I knew the correct expression. I redid the squaring and rearranging when I was following LCKurtz's hint. :)

    I shouldn't be posting questions in the midnight. :tongue:
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