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How to solve (x-1)^2 * (a+x)=1

  1. Jan 21, 2009 #1
    I am a little bit confused about solving the following equation:


    How to do this??
  2. jcsd
  3. Jan 21, 2009 #2
    Are you sure there's a simple way to solve that, given that you don't know a? It's a cubic...
  4. Jan 21, 2009 #3
    well, actually this is the original equation (see figure1)

    The solution is in figure 2..

    So let me reformulate my question: Can this be proven analytically?

    Attached Files:

  5. Jan 21, 2009 #4


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    This is very different from the problem in your first post!

    Anyways, start by squaring both sides of the equation in the first link. Then multiply both sides by [tex]4((\rho^{*})^2+(x^{*})^2)[/tex] and simplify to obtain:


    That should tell you that either [tex](\rho^{*})^2=0[/tex] or


    You can use the quadratic equation to solve the above expression for [tex](\rho^{*})^2[/tex] and then take the square root to obtain the final solution.
  6. Jan 22, 2009 #5
    Yes, ok thank you. It did not cross my mind to substitute a variable for a variable^2
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