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## 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^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