Solve $ \begin{matrix} -1-\frac{1}{kx_1}+\frac{1}{k(1-x_1-x_2)}=0\\ 3x_2^2-2-\frac{1}{kx_2}+\frac{1}{k(1-x_1-x_2)}=0\\ \end{matrix} $

Question

Solve $$ \begin{matrix} -1-\frac{1}{kx_1}+\frac{1}{k(1-x_1-x_2)}=0\\ 3x_2^2-2-\frac{1}{kx_2}+\frac{1}{k(1-x_1-x_2)}=0\\ \end{matrix} $$ in terms of k.

I just got $$ \begin{matrix} x_1=\frac{x_2}{kx_2+1-3kx_2^3}\\ x_2=1-x_1-\frac{x_1}{kx_1+1}\\ \end{matrix} $$ But I don't know how to go further and I'm not sure if I'm on the right track. Can anyone help me solve this? Thanks in advance.

Answer 1

Hint: solving your second equation for $x_1$ we get $$x_1=-3x_2^4k+3x_2^3k+3kx_2^2+2kx_2+2x_2-1$$ plugging this in your first equation you will get an equation only in $x_2$