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Math Help - Need help with this math problem

  1. #1
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    Need help with this math problem

    Hey there I need some help with this problem

    Find x^2 + y^2 if x,y N and xy + x + y = 71 and (x^2)y + x(y^2) = 880

    I've been working on this for hours still no luck, hoping someone can show me how to solve this problem thanks.
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  2. #2
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    Re: Need help with this math problem

    Quote Originally Posted by gfbrd View Post
    Find x^2 + y^2 if x,y N and xy + x + y = 71 and (x^2)y + x(y^2) = 880
    (xy+x+y)^2=x^2y^2+x^2+y^2+2x^2y+2xy^2+2xy=(71)^2
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  3. #3
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    Re: Need help with this math problem

    I did that already and got stuck a bit farther after that
    what I did was substituted those x^2y and xy^2 with 880 to get

    x^2(y^2) + x^2 + y^2 + 880 + 880 + 2xy = 71^2

    and I noticed
    x^2(y^2)((x+y)^2) = 880^2

    I had a bit of trouble after that
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  4. #4
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    Re: Need help with this math problem

    What I did was to substitute u = xy and w = x + y

    Then we have

    u = 71 - x - y = 71 - w
    and also
    u = (880)/(x + y) = (880)/w

    Now you can eliminate u and you'll have a quadratic you can solve for w.

    Also, you may have noticed that x and y are symmetric. They appear in the same way in both equations, so if (a , b) is a solution, (b , a) should be also.

    I assume that's enough for now? Write back please if you still have any trouble.
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  5. #5
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    Re: Need help with this math problem

    hey zhandele thanks for the hint but after doing what you told me I came up with 2 answers:

    xy = 16 = 55 is this supposed to be like this or is there 1 solution? im not sure which one to pick but after substituting in both of them I get

    x^2 + y^2 = 3493 = 646
    yea I get 2 solutions here, let me know if this is correct or not thanks
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  6. #6
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    Re: Need help with this math problem

    Here's my understanding.

    If x + y = 55 then xy = 16. This leads to two answers, but they're irrational. They involve the square root of 329, as I recall. I believe you're supposed to look for integers, so these answers you don't want.

    If x + y = 16 then xy = 55. You can then solve for x = 5 or x = 11 and for y = 5 and x = 11. If you substitute back, I think you'll find either pair will work, so I suppose you can you have two answers.

    The way I see it, these two answers aren't really different. That's what I meant when I said that x and y are symmetric. Maybe that wasn't the best way to put it. If you substitute x for y and y for x, nothing about the problem changes, it looks just the same. Did you try graphing the two lines and two hyperbolas? They're all symmetric about the line y = x.

    If you were doing a story problem, where x and y stood for something in the real world, so somebody cared whether you used five or eleven of x, then I'd say they're different answers.

    Perhaps that's why you're asked for x^2 + y^2. The sum is the same no matter which is the 5. BTW, I get

    x^2 + y^2 = 146

    How did you get that 646?

    I'd say 146 is the answer you want.

    Kindly, R
    Thanks from gfbrd
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  7. #7
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    Re: Need help with this math problem

    I got it now thanks for your help
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