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- Feb 14, 2012

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For the first time I found a system of equations where I'm at my wit's end and don't know how to solve it, no matter how hard I tried...

Problem:

Solve

\(\displaystyle z^2+2xyz=1\)

\(\displaystyle 3x^2y^2+3xy^2=1+x^3y^4\)

\(\displaystyle z+zy^4+4y^3=4y+6y^2z\)

Attempt:

I tried to eliminate the variable $z$ and obtained another equation in terms of $x$ and $y$ but I think you'll agree with me that I'm headed in the wrong direction after you saw the equation I found...

\(\displaystyle \left(\frac{4y(1-y^2)}{y^4-6y^2+1} \right)^2+2xy\left(\frac{4y(1-y^2)}{y^4-6y^2+1} \right)=1\)

I'd appreciate any hints anyone could give me on this problem.

Thanks in advance.