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Solve in R (inequalities)

  1. Apr 21, 2013 #1
    1. The problem statement, all variables and given/known data
    x y and z are real numbers
    solve in lR
    (1+4x^2)y=4z^2
    (1+4y^2)z=4x^2
    (1+4z^2)x=4y^2


    2. The attempt at a solution
    (1+4x^2)y(1+4y^2)z(1+4z^2)x=64x^2y^2z^2(x and y and z =/=0)
    ([itex]\frac{1}{4}[/itex]+x^2)([itex]\frac{1}{4}[/itex]+y^2)([itex]\frac{1}{4}[/itex]+z^2)=xyz
    now i can tell from this that (1/2,1/2,1/2)(suppose that x=y=z solves this also (0,0,0,) is a solution)
    but i'm really stuck here i thought this problem would be easy i need help
     
  2. jcsd
  3. Apr 21, 2013 #2

    mfb

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    2016 Award

    Staff: Mentor

    I would try this: plugging (1) in (3), (1+(1+4x^2)y)x=4y^2 or 4y^2-(x+4x^3)y-x=0
    This can be solved for y.
     
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