# Solve in R (inequalities)

1. Apr 21, 2013

### Andrax

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)
($\frac{1}{4}$+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

2. Apr 21, 2013

### 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.