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Can This be Simplified or Solved?

  1. Dec 17, 2014 #1
    1. The problem statement, all variables and given/known data
    x^4 + y^4 - xy^2 = x^2y


    2. Relevant equations
    None. However, I'm using "^" to represent an exponent operation.

    3. The attempt at a solution
    Not sure. That's why I'm asking. It just feels to me that everything is an unlike term and thus you can't do anything.

    Is that correct here? Thanks for the help everyone!
     
  2. jcsd
  3. Dec 17, 2014 #2

    haruspex

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    How do you mean 'solved'? Do you mean finding roots?
    Is this the whole question as given to you? If not, please post the original question.
     
  4. Dec 18, 2014 #3

    statdad

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    You can do a little factoring by subtracting a convenient amount from each side, but without knowing what your goal is I'm not sure what benefit would result.
     
  5. Dec 18, 2014 #4

    berkeman

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    If I understand what you wrote, it looks like x=y=1 is a solution by inspection. Where is the equation from?
     
  6. Dec 18, 2014 #5

    Mark44

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    As are x = 0, y = 0.
     
  7. Dec 19, 2014 #6

    LCKurtz

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    Here's a graph, for what it's worth. I've included ##y=\pm x## in the picture:
    graph.jpg
    Click on it for a better view.
     
  8. Dec 19, 2014 #7

    berkeman

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    Very Cool :-)
     
  9. Dec 27, 2014 #8
    First, Merry Christmas! lol.

    I just logged back in here after getting bored today and wanting to catch up on my threads! Sorry it's taken so long, but thanks for the answers!

    As for the "original question," this is what was written on the board of our class by some girl doing some stuff after class. It's not from any worksheet I had from the class (I even doubled-chcked), but was just a random "problem" I saw on the board and was puzzled by when I glanced at it and thought I'd jot it down.

    My question is whether anything can be done arithmetic-wise to combine what seem like unlike terms? And also, can the equation be solved above in any way?
     
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