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Sum of roots

  1. Aug 24, 2015 #1
    Given two numbers: [tex] A + \sqrt{A^2 - B^2}[/tex] and [tex] U + \sqrt{U^2 - V^2}[/tex] OBS: A, B, U and V are real numbers.

    I want sum it and express the result in the same form: [tex] A + \sqrt{A^2 - B^2} + U + \sqrt{U^2 - V^2} = x + \sqrt{x^2 - y^2}[/tex] So, x depends of A and U. And y depends of B and V:
    [tex] x = x(A, U)[/tex] [tex] y = y(B, V)[/tex] Do have any ideia about how do it?

    PS: A is the arithmetic mean of the roots of the quadratic equation and B is the geometric mean. Is a nice expression for the quadratic formula!
     
  2. jcsd
  3. Aug 24, 2015 #2

    mfb

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    2016 Award

    Staff: Mentor

    There is no unique solution. You can simply set x=y= [left side of the equation], for example. And I don't see any special solution sticking out.
     
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