- #1
anemone
Gold Member
MHB
POTW Director
- 3,883
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Hi MHB,
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.:)
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.:)