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Solve equation

  1. Jan 23, 2010 #1
    1. The problem statement, all variables and given/known data

    how to solve this:

    4x3 + 4y =0
    4y3 + 4x =0


    the solution is x = 0,1,-1
    y = 0,-1,1

    how did they bring such result :bugeye:
     
  2. jcsd
  3. Jan 23, 2010 #2
    Find y from the first equation and then plug it into the second one so you're done!

    AB
     
  4. Jan 23, 2010 #3
    4x3 + 4y =0
    x3 + y=0
    y=x3

    NOW........... plugging in

    4y3 + 4x =0
    y3 + x=0
    (x3)3 + x = 0

    now what?? how do i continue from here :S
     
  5. Jan 23, 2010 #4

    vela

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    First, fix your algebra mistake. You dropped a sign. Once you fix that, you'll find you can factor the polynomial and solve for its roots.
     
  6. Jan 23, 2010 #5
    4x3 + 4y =0
    x3 + y=0
    y=-x3

    NOW........... plugging in

    4y3 + 4x =0
    y3 + x=0
    (-x3)3 + x = 0

    Please i am stuck show me how, i know it should be factored by x but how?
     
    Last edited: Jan 23, 2010
  7. Jan 23, 2010 #6

    vela

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    First, simplify (-x3)3. What do you get?
     
  8. Jan 23, 2010 #7
    -x9 + x = 0

    now what?
     
  9. Jan 23, 2010 #8
    -x9 + x = 0
    x(-x8 + 1) = 0

    x = 0 or x= 1 right?
     
  10. Jan 23, 2010 #9

    vela

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    You can flip the sign of the whole equation to make it a little simpler to work with:

    x9-x=0

    Now you have a common factor of x in both terms, so factor it out.

    OK, you posted while I was writing. :) So you have

    x(x8-1) = 0

    So this means x=0 or x8-1=0, right? So you have one of the roots so far.

    Note that x8-1=(x4)2-12 is a difference of squares, so what does it factor into?
     
  11. Jan 23, 2010 #10
    Thank you so much, very appreciated!
     
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