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Homework Help: Need Help w/ x^2-xy+y^2+x+y+1=0

  1. Nov 3, 2009 #1
    I need help with this Problem x^2-xy+y^2+x+y+1=0. It is part of a math project I am doing to plot a graph. The original problem was x^3+3xy+y^3=1 can factor and it plots a line at a 45 degree angle. The first part of the factorization is x+y-1=0. The only thing I can figure to do with the problem is to take the +1 and move it to the otherside of the = and make it -1 so I have a point to work with other than 0. The only number I have found that will equal -1 is to have both x and y as -1. Any help would be gladly received. Thanks for your time.

    P.S. I am only in Intermediate Algerbra so please make it so I can understand.
  2. jcsd
  3. Nov 3, 2009 #2


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    You started with your original equation:
    x3+3xy+y3 - 1 = 0
    and factored it to get:

    (x + y - 1)(x2 -xy+y2+x+y+1) = 0

    and have used the first factor to get the straight line. So your remaining problem is to see if the other factor gives you anything:

    x2- xy+y2+x+y+1 = 0

    This is a quadratic equation in y which you can solve by the quadratic formula. So collect terms on powers of y and look at the discriminant of that quadratic equation. If the discriminant is negative you get no graph. If it is positive the quadratic formula will give you a formula for y.
  4. Nov 8, 2009 #3


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    If you're confused with what to do with the quadratic, as an alternative, try expanding:


    and see if you can deduce anything from that.
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