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Simultaneous non-linear equations

  1. Apr 24, 2005 #1

    HallsofIvy

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    This was sent to me as a personal message- it's always better to post questions like this than just send them to me!
     
  2. jcsd
  3. Apr 24, 2005 #2

    arildno

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    abi ubong, hint:
    Try to find all positve integer solutions to your system;
    that is what I think your teacher is after!

    1.So, your first job is to determine:
    Which pairs of positive integers (x,y) satisfies the equation: x+y=5

    2. Then, you must determine: Which of those pairs you found under 1. also satisfy [tex]x^{x}+y^{y}=31[/tex]
     
  4. Apr 24, 2005 #3

    HallsofIvy

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    Are you certain you copied this correctly? x+y= 5, x2+ y2= 31 would be very easy, x+ y= 5, xx+ yy= 31 is very hard!

    The obvious thing to do is write the first equation as y= 5- x and substitute into the second equation: xx+ (5-x)5-x= 31. You might be able to put this into a form you could apply the "Lambert W function" to, but that's certainly not elementary. Other than that, I would suggest a numerical solution.

    Arildno got in before me- his suggestion: look for positive integer solutions reduces the possible solutions so it can be done by direct computation.
    Assuming, of course, that there are positive integer solutions!
     
    Last edited: Apr 24, 2005
  5. Apr 24, 2005 #4

    saltydog

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    I aint' proud. Am I helping out too much? Really, I didnt' even know to check for integers until I gave up and scrolled down to Arildno's post. Anyway, the plot is for:

    [tex]y(x)=x^x+(5-x)^{5-x}-31[/tex]
     

    Attached Files:

  6. Apr 24, 2005 #5

    arildno

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    Just to add something in regard to saltydog's post (I hope he'll agree with me on this):
    abi ubong:
    The roots of saltydog's FUNCTION Y(x) will give you the NUMBERS x in the NUMBER PAIRS (x,y) which are solutions to your system.
    The corresponding NUMBERS y is found by the equation y=5-x, where x is a root for Y(x).
     
  7. Apr 24, 2005 #6
    i still do not get any of this especially urs hallsofivy wats rthe lambert w function or watever it is ,plssssssssssssss i need graet help
     
  8. Apr 24, 2005 #7

    arildno

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    Well, since you evidently haven't bothered to read my reply to you, don't expect anymore help on this.
     
    Last edited: Apr 24, 2005
  9. Apr 24, 2005 #8

    HallsofIvy

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    abia ubong: The "Lambert W function" is the inverse of the function f(x)= xex. It can be used to solve many equations in which x is both an exponent and a base.

    However, if you are not in college, you probably would not be expected to know that function. Look at "salty dog"'s and "arildno"'s responses!

    Look again at arildno's first suggestion. If x and y have to be positive integers AND their sum is 5, the only possibilities are:
    x= 1, y= 4
    x= 2, y= 3
    x= 3, y= 2
    x= 4, y= 1

    Do any of those satisfy xx+ yy= 31?
     
    Last edited: Apr 24, 2005
  10. Apr 27, 2005 #9
    hey firstly do not get offended arildno,also hallsofivy wat if x or y or maybe both were 2 be negative,such methods might not work i need a general solution .
    thnxs
     
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