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Homework Help: Equation solving

  1. Jun 14, 2010 #1
    1. The problem statement, all variables and given/known data
    The equation is:[tex]\frac{(a-x)^4+(x-b)^4}{(a+b-2x)^2}=\frac{a^4+b^4}{(a+b)^2}[/tex]

    2. Relevant equations

    3. The attempt at a solution

    I expanded the terms on the L.H.S and ended up with an equation of 4th,3rd,2nd ,1st degree equation very difficult to solve.
  2. jcsd
  3. Jun 14, 2010 #2
    Am I correct to assume that you are suppose to find a solution with respect to x?

    I get that x is either [tex]x = \frac{2ab}{a+b}[/tex] or [tex]\frac{a^2+b^2}{a+b}[/tex] or x = 0

    just remember that [tex](a-x)^4 = ((a-x)^2)^2[/tex]
    Last edited: Jun 14, 2010
  4. Jun 14, 2010 #3

    Yes you right ,but how did you get those solutions?

    But is it not there a forth solution ,or one of them is double??
  5. Jun 14, 2010 #4
    1) Use the fact that (x-a)^4 = ((x-a)^2)^2 and then solve with respect to x
  6. Jun 14, 2010 #5
    I am sorry can you elaborate a little more ,i cannot follow.
  7. Jun 15, 2010 #6
    Sorry I didn't report back to yesterday had an upset stomac :(

    You expand the lefthand side as I showed you and then solve it respect to x.
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