1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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

    Mentallic

    User Avatar
    Homework Helper

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

    [tex]\frac{1}{2}\left((x-y)^2+(x+1)^2+(y+1)^2\right)[/tex]

    and see if you can deduce anything from that.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Need Help w/ x^2-xy+y^2+x+y+1=0
  1. Y = x^2-a(x+1)+3 (Replies: 9)

Loading...