Can the System of Inequalities in R be Solved with Real Numbers x, y, and z?

[Andrax]

Homework Statement

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^22. 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)
(\frac{1}{4}+x^2)(\frac{1}{4}+y^2)(\frac{1}{4}+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

 

[mfb]

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.