Tricky simultaneous equation

[mrpace]

Hi there

At first glance I thought this seemed fairly easy, but it gets messy really quick

Solve:

x^2 - yz = 1
y^2 - xz = 2
z^2 - xy = 3


Help is appreciated
Thanks

 

[Cubist]

You didn't show any of your work...

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I don't know if there's an elegant solution to this. Where did you decide to give up, and why? You can post a photo of your work.